The Scala Language Specification

Home , Guard (computer science), Whitespace character

The Scala Language Speciﬁcation Version 1.0

DRAFT November 16, 2005

Martin Odersky Philippe Altherr Vincent Cremet Burak Emir Stéphane Micheloud Nikolay Mihaylov Michel Schinz Erik Stenman Matthias Zenger

PROGRAMMING METHODS LABORATORY EPFL SWITZERLAND

Contents

I Rationale 1

II The Scala Language Speciﬁcation 7

1 Lexical Syntax 9 1.1 Identiﬁers ...... 10 1.2 Braces and Semicolons ...... 11 1.3 Literals ...... 11 1.4 Whitespace and Comments ...... 11 1.5 XML mode ...... 12

2 Identiﬁers, Names and Scopes 13

3 Types 15 3.1 Paths ...... 16 3.2 Value Types ...... 16 3.2.1 Singleton Types ...... 16 3.2.2 Type Projection ...... 16 3.2.3 Type Designators ...... 17 3.2.4 Parameterized Types ...... 17 3.2.5 Compound Types ...... 18 3.2.6 Function Types ...... 18 3.3 Non-Value Types ...... 19 3.3.1 Method Types ...... 19 3.3.2 Polymorphic Method Types ...... 19 3.4 Base Classes and Member Deﬁnitions ...... 20 3.5 Relations between types ...... 22 iv CONTENTS

3.5.1 Type Equivalence ...... 22 3.5.2 Conformance ...... 22 3.6 Type Erasure ...... 24 3.7 Implicit Conversions ...... 24

4 Basic Declarations and Definitions 27 4.1 Value Declarations and Definitions ...... 28 4.2 Variable Declarations and Definitions ...... 29 4.3 Type Declarations and Type Aliases ...... 30 4.4 Type Parameters ...... 32 4.5 Function Declarations and Definitions ...... 34 4.6 Overloaded Definitions ...... 36 4.7 Import Clauses ...... 36

5 Classes and Objects 39 5.1 Templates ...... 39 5.1.1 Constructor Invocations ...... 40 5.1.2 Base Classes ...... 40 5.1.3 Evaluation ...... 41 5.1.4 Template Members ...... 42 5.1.5 Overriding ...... 42 5.1.6 Modifiers ...... 43 5.1.7 Attributes ...... 45 5.2 Class Definitions ...... 46 5.2.1 Constructor Definitions ...... 47 5.2.2 Case Classes ...... 48 5.3 Traits ...... 50 5.4 Object Definitions ...... 51

6 Expressions 53 6.1 Literals ...... 54 6.2 Designators ...... 55 6.3 This and Super ...... 55 6.4 Function Applications ...... 57 CONTENTS v

6.5 Type Applications ...... 58 6.6 References to Overloaded Bindings ...... 58 6.7 Instance Creation Expressions ...... 60 6.8 Blocks ...... 60 6.9 Prefix, Infix, and Postfix Operations ...... 61 6.10 Typed Expressions ...... 62 6.11 Method closures ...... 63 6.12 Assignments ...... 63 6.13 Conditional Expressions ...... 65 6.14 While Loop Expressions ...... 65 6.15 Do Loop Expressions ...... 66 6.16 Comprehensions ...... 66 6.17 Return Expressions ...... 68 6.18 Throw Expressions ...... 68 6.19 Try Expressions ...... 69 6.20 Anonymous Functions ...... 69 6.21 Statements ...... 70

7 Pattern Matching 73 7.1 Patterns ...... 73 7.1.1 Regular Pattern Matching ...... 74 7.2 Pattern Matching Expressions ...... 77

8 Views 79 8.1 View Deﬁnition ...... 79 8.2 View Application ...... 79 8.3 Finding Views ...... 80 8.4 View-Bounds ...... 81 8.5 Conditional Views ...... 84

9 Top-Level Deﬁnitions 85 9.1 Packagings ...... 85

10 Local Type Inference 87 vi CONTENTS

11 XML expressions and patterns 89 11.1 XML expressions ...... 89 11.2 XML patterns ...... 91

12 The Scala Standard Library 93 12.1 Root Classes ...... 93 12.2 Value Classes ...... 95 12.2.1 Class Double ...... 95 12.2.2 Class Float ...... 95 12.2.3 Class Long ...... 96 12.2.4 Class Int ...... 96 12.2.5 Class Short ...... 97 12.2.6 Class Char ...... 97 12.2.7 Class Short ...... 97 12.2.8 Class Boolean ...... 98 12.2.9 Class Unit ...... 98 12.3 Standard Reference Classes ...... 98 12.3.1 Class String ...... 98 12.3.2 The Tuple classes ...... 99 12.3.3 The Function Classes ...... 99 12.3.4 Class Array ...... 99 12.4 The Predef Object ...... 100 12.5 Class Node ...... 101

A Scala Syntax Summary 105

B Implementation Status 111 IRATIONALE

There are hundreds of programming languages in active use, and many more are being designed each year. It is therefore hard to justify the development of yet another language. Nevertheless, this is what we attempt to do here. Our argument is based on two claims:

Claim 1: The raise in importance of web services and other distributed soft- ware is a fundamental paradigm shift in programming. It is comparable in scale to the shift 20 years ago from character-oriented to graphical user interfaces. Claim 2: That paradigm shift will provide demand for new programming languages, just as graphical user interfaces promoted the adoption of object- oriented languages.

For the last 20 years, the most common programming model was object-oriented: System components are objects, and computation is done by method calls. Meth- ods themselves take object references as parameters. Remote method calls let one extend this programming model to distributed systems. The problem of this model is that it does not scale up very well to wide-scale networks where messages can be delayed and components may fail. Web services address the message delay problem by increasing granularity, using method calls with larger, structured arguments, such as XML trees. They address the failure problem by using transparent replica- tion and avoiding server state. Conceptually, they are tree transformers that con- sume incoming message documents and produce outgoing ones. Why should this have an effect on programming languages? There are at least two reasons: First, today’s object-oriented languages are not very good at analyzing and transforming XML trees. Because such trees usually contain data but no methods, they have to be decomposed and constructed from the “outside”, that is from code which is external to the tree definition itself. In an object-oriented language, the ways of doing so are limited. The most common solution [W3Ca] is to represent trees in a generic way, where all tree nodes are values of a common type. This makes it easy to write generic traversal functions, but forces applications to operate on a very low conceptual level, which often loses important semantic distinctions present in the XML data. More semantic precision is obtained if different internal types model different kinds of nodes. But then tree decompositions require the use of run-time type tests and type casts to adapt the treatment to the kind of node en- countered. Such type tests and type casts are generally not considered good object- oriented style. They are rarely efficient, nor easy to use. By contrast, tree transformation is the natural domain of functional languages. Their algebraic data types, pattern matching and higher-order functions make these languages ideal for the task. It’s no wonder, then, that specialized languages for transforming XML data such as XSLT are functional. Another reason why functional language constructs are attractive for web-services is that mutable state is problematic in this setting. Components with mutable state 4 are harder to replicate or to restore after a failure. Data with mutable state is harder to cache than immutable data. Functional language constructs make it relatively easy to construct components without mutable state. Many web services are constructed by combining different languages. For instance, a service might use XSLT to handle document transformation, XQuery for database access, and Java for the “business logic”. The downside of this approach is that the necessary amount of cross-language glue can make applications cumbersome to write, verify, and maintain. A particular problem is that cross-language interfaces are usually not statically typed. Hence, the benefits of a static type system are missing where they are needed most – at the join points of components written in different paradigms. Conceivably, the glue problem could be addressed by a “multi-paradigm” language that would express object-oriented, concurrent, as well as functional aspects of an application. But one needs to be careful not to simply replace cross-language glue by awkward interfaces between different paradigms within the language itself. Ideally, one would hope for a fusion which unifies concepts found in different paradigms instead of an agglutination, which merely includes them side by side. This fusion is what we try to achieve with Scala 1. Scala is both an object-oriented and functional language. It is a pure object- oriented language in the sense that every value is an object. Types and behavior of objects are described by classes. Classes can be composed using mixin composition. Scala is designed to work seamlessly with mainstream object-oriented languages, in particular Java and C#. Scala is also a functional language in the sense that every function is a value. Nesting of function definitions and higher-order functions are naturally supported. Scala also supports a general notion of pattern matching which can model the algebraic types used in many functional languages. Furthermore, this notion of pattern matching naturally extends to the processing of XML data. The design of Scala is driven by the desire to unify object-oriented and functional elements. Here are three examples how this is achieved:

• Since every function is a value and every value is an object, it follows that every function in Scala is an object. Indeed, there is a root class for functions which is specialized in the Scala standard library to data structures such as arrays and hash tables. • Data structures in many functional languages are defined using algebraic data types. They are decomposed using pattern matching. Object-oriented languages, on the other hand, describe data with class hierarchies. Algebraic data types are usually closed, in that the range of alternatives of a type is fixed when the type is defined. By contrast, class hierarchies can be extended by adding new leaf classes. Scala adopts the object-oriented class hierarchy scheme for

1Scala stands for “Scalable Language”. The term means “Stairway” in Italian 5

data definitions, but allows pattern matching against values coming from a whole class hierarchy, not just values of a single type. This can express both closed and extensible data types, and also provides a convenient way to ex- ploit run-time type information in cases where static typing is too restrictive. • Module systems of functional languages such as SML or Caml excel in abstraction; they allow very precise control over visibility of names and types, including the ability to partially abstract over types. By contrast, object-oriented languages excel in composition; they offer several composition mechanisms lacking in module systems, including inheritance and unlimited recursion between objects and classes. Scala unifies the notions of object and module, of module signature and interface, as well as of functor and class. This combines the abstraction facilities of functional module systems with the composition constructs of object-oriented languages. The unification is made possible by means of a new type system based on path-dependent types [OCRZ03].

There are several other languages that try to bridge the gap between the functional and object oriented paradigms. Smalltalk[GR83], Python[vRD03], or Ruby[Mat01] come to mind. Unlike these languages, Scala has an advanced static type system, which contains several innovative constructs. This aspect makes the Scala deﬁni- tion a bit more complicated than those of the languages above. On the other hand, Scala enjoys the robustness, safety and scalability beneﬁts of strong static typing. Furthermore, Scala incorporates recent advances in type inference, so that exces- sive type annotations in user programs can usually be avoided.

IITHE SCALA LANGUAGE SPECIFICATION

Chapter 1 Lexical Syntax

Scala programs are written using the Unicode character set. This chapter deﬁnes the two modes of Scala’s lexical syntax, the Scala mode and the XML mode. If not otherwise mentioned, the following descriptions of Scala tokens refer to Scala mode, and literal characters ‘c’ refer to the ASCII fragment \u0000-\u007F. In Scala mode, Unicode escapes are replaced by the corresponding Unicode character with the given hexadecimal code.

UnicodeEscape ::= \{\\}u{u} HexDigit HexDigit HexDigit HexDigit HexDigit ::= ’0’ | ... | ‘9’ | ‘A’ | ... | ‘F’ | ‘a’ | ... | ‘f’ |

To construct tokens, characters are distinguished according to the following classes (Unicode general category given in parentheses):

1. Whitespace characters. \u0020 | \u0009 | \u000D | \u000A 2. Letters, which include lower case letters(Ll), upper case letters(Lu), title- case letters(Lt), other letters(Lo), letter numerals(Nl) and the two characters \u0024 ‘$’ and \u005F ‘_’, which both count as upper case letters 3. Digits ‘0’ | ... | ‘9’. 4. Parentheses ‘(’ | ‘)’ | ‘[’ | ‘]’ | ‘{’ | ‘}’. 5. Delimiter characters ‘‘’ | ‘’’ | ‘"’ | ‘.’ | ‘;’ | ‘,’. 6. Operator characters. These consist of all printable ASCII characters \u0020-\u007F. which are in none of the sets above, mathematical symbols(Sm) and other symbols(So). 10 Lexical Syntax

1.1 Identiﬁers

Syntax:

op ::= special {special} varid ::= lower idrest id ::= upper idrest | varid | op | ‘‘‘string chars‘’’ idrest ::= {letter digit} [‘_’ op | ‘_’ idrest] | There are three ways to form an identifier. First, an identifier can start with a letter which can be followed by an arbitrary sequence of letters and digits. This may be followed by underscore ‘_’ characters and other string composed of either letters and digits or of special characters. Second, an identifier can start with a special character followed by an arbitrary sequence of special characters. Finally, an identifier may also be formed by an arbitrary string between back-quotes (host systems may impose some restrictions on which strings are legal for identifiers). As usual, a longest match rule applies. For instance, the string

big_bob++=‘def‘ decomposes into the three identifiers big_bob, ++=, and def. The rules for pattern matching further distinguish between variable identifiers, which start with a lower case letter, and constant identifiers, which do not. The ‘$’ character is reserved for compiler-synthesized identifiers. User programs are not allowed to define identifiers which contain ‘$’ characters. The following names are reserved words instead of being members of the syntactic class id of lexical identifiers.

abstract case catch class def do else extends false final finally for if implicit import match new null object override package private protected return sealed super this throw trait try true type val var while with yield _ : = => <- <: >: # @

The Unicode operator \u21D2 ‘ ’ has the ASCII equivalent ‘ ’, which is also re- ⇒ => served.

Example 1.1.1 Here are examples of identiﬁers: 1.2 Braces and Semicolons 11

x Object maxIndex p2p empty_? + +_field αρ²τη

1.2 Braces and Semicolons

A semicolon ‘;’ is implicitly inserted after every closing brace if there is a new line character between closing brace and the next regular token after it, except if that token cannot legally start a statement. The tokens which cannot legally start a statement are the following delimiters and reserved words:

catch else extends finally with yield , . ; : = => <- <: <% >: # @ ) ] }

1.3 Literals

There are literals for integer numbers (of types Int and Long), ﬂoating point numbers (of types Float and Double), characters, and strings. The syntax of these literals is in each case as in Java. Syntax:

intLit ::= “as in Java” floatLit ::= “as in Java” charLit ::= “as in Java” stringLit ::= “as in Java”

1.4 Whitespace and Comments

Tokens may be separated by whitespace characters and/or comments. Comments come in two forms: A single-line comment is a sequence of characters which starts with // and extends to the end of the line.

A multi-line comment is a sequence of characters between /* and */. Multi-line comments may be nested. 12 Lexical Syntax

1.5 XML mode

In order to allow literal inclusion of XML fragments, lexical analysis switches from Scala mode to XML mode when encountering an opening angle bracket ’<’ in the following circumstance: The ’<’ must be preceded either by whitespace, an opening parenthesis or an opening brace and immediately followed by a character starting an XML name. Syntax:

( whitespace | ’(’ | ’{’ ) ’<’ XNameStart

XNameStart ::= ‘_’ | BaseChar | Ideographic (as in W3C XML, but without ‘:’

The scanner switches from XML mode to Scala mode if either

• the XML expression or the XML pattern started by the initial ’<’ has been suc- cessfully parsed, or if • the parser encounters an embedded Scala expression or pattern and forces the Scanner back to normal mode, until the Scala expression or pattern is suc- cessully parsed. In this case, since code and XML fragments can be nested, the parser has to maintain a stack that reﬂects the nesting of XML and Scala expressions adequately.

Note that no Scala tokens are constructed in XML mode, and that comments are interpreted as text. Chapter 2 Identiﬁers, Names and Scopes

Names in Scala identify types, values, methods, and classes which are collectively called entities. Names are introduced by definitions, declarations (§4) or import clauses (§4.7), which are collectively called binders. There are two different name spaces, one for types (§3) and one for terms (§6). The same name may designate a type and a term, depending on the context where the name is used. A definition or declaration has a scope in which the entity defined by a single name can be accessed using a simple name. Scopes are nested, and a definition or declaration in some inner scope shadows a definition in an outer scope that contributes to the same name space. Furthermore, a definition or declaration shadows bindings introduced by a preceding import clause, even if the import clause is in the same block. Import clauses, on the other hand, only shadow bindings introduced by other import clauses in outer blocks. A reference to an unqualified (type- or term-) identifier x is bound by the unique binder, which

• defines an entity with name x in the same namespace as the identifier, and • shadows all other binders that define entities with name x in that namespace.

It is an error if no such binder exists. If x is bound by an import clause, then the simple name x is taken to be equivalent to the qualiﬁed name to which x is mapped by the import clause. If x is bound by a deﬁnition or declaration, then x refers to the entity introduced by that binder. In that case, the type of x is the type of the referenced entity.

Example 2.0.1 Consider the following nested deﬁnitions and imports:

object m1 { 14 Identiﬁers, Names and Scopes

object m2 { val x: int = 1; val y: int = 2 } object m3 { val x: boolean = true; val y: String = "" } val x: int = 3; { import m2._; // shadows nothing // reference to ‘x’ is ambiguous here val x: String = "abc"; // shadows preceding import // name ‘x’ refers to latest val definition { import m3._ // shadows only preceding import m2 // reference to ‘x’ is ambiguous here // name ‘y’ refers to latest import clause } } }

A reference to a qualified (type- or term-) identifier e.x refers to the member of the type T of e which has the name x in the same namespace as the identifier. It is an error if T is not a value type (§3.2). The type of e.x is the member type of the referenced entity in T . Chapter 3 Types

Syntax:

Type ::= Type1 ‘=>’ Type | ‘(’ [Types] ‘)’ ‘=>’ Type | Type1 Type1 ::= SimpleType {with SimpleType} [Refinement] SimpleType ::= StableId | SimpleType ‘#’ id | Path ‘.’ type | SimpleType TypeArgs | ‘(’ Type ’)’ Types ::= Type {‘,’ Type}

We distinguish between first-order types and type constructors, which take type parameters and yield types. A subset of first-order types called value types represents sets of (first-class) values. Value types are either concrete or abstract. Every concrete value type can be represented as a class type, i.e. a type designator (§3.2.3) that refers to a class1 (§5.2), or as a compound type (§3.2.5) consisting of class types and possibly also a refinement (§3.2.5) that further constrains the types of its members. A shorthand exists for denoting function types (§3.2.6). Abstract value types are introduced by type parameters and abstract type bindings (§4.3). Parentheses in types are used for grouping. Non-value types capture properties of identifiers that are not values (§3.3). There is no syntax to express these types directly in Scala.

1We assume that objects and packages also implicitly deﬁne a class (of the same name as the object or package, but inaccessible to user programs). 16 Types

3.1 Paths

Syntax:

StableId ::= id | Path ‘.’ id | [id ’.’] super [‘[’ id ‘]’] ‘.’ id Path ::= StableId | [id ‘.’] this

Paths are not types themselves, but they can be a part of named types and in that way form a central role in Scala’s type system. A path is one of the following.

• The empty path ² (which cannot be written explicitly in user programs).

• C .this, where C references a class. The path this is taken as a shorthand for C .this where C is the name of the class directly enclosing the reference.

• p.x where p is a path and x is a stable member of p. Stable members are members introduced by value or object deﬁnitions, as well as packages.

• C .super.x or C .super[M ].x where C references a class and x references a stable member of the super class or designated mixin class M of C. The preﬁx super is taken as a shorthand for C .super where C is the name of the class directly enclosing the reference.

A stable identiﬁer is a path which ends in an identiﬁer.

3.2 Value Types

3.2.1 Singleton Types

Syntax:

SimpleType ::= Path ‘.’ type

A singleton type is of the form p.type, where p is a path pointing to a value expected to conform to scala.AnyRef. The type denotes the set of values consisting of the value denoted by p and null.

3.2.2 Type Projection

Syntax:

SimpleType ::= SimpleType ‘#’ id 3.2 Value Types 17

A type projection T #x references the type member named x of type T . T must be either a singleton type, or a non-abstract class type, or a Java class type (in either of the last two cases, it is guaranteed that T has no abstract type members).

3.2.3 Type Designators

Syntax:

SimpleType ::= StableId

A type designator refers to a named value type. It can be simple or qualified. All such type designators are shorthands for type projections. Specifically, the unqualified type name t where t is bound in some class, object, or package C is taken as a shorthand for C .this.type#t. If t is not bound in a class, object, or package, then t is taken as a shorthand for ².type#t. A qualified type designator has the form p.t where p is a path (§3.1) and t is a type name. Such a type designator is equivalent to the type projection p.type#x.

Example 3.2.1 Some type designators and their expansions are listed below. We assume a local type parameter t, a value maintable with a type member Node and the standard class scala.Int,

t ².type#t Int scala.type#Int scala.Int scala.type#Int data.maintable.Node data.maintable.type#Node

3.2.4 Parameterized Types

Syntax:

SimpleType ::= SimpleType TypeArgs TypeArgs ::= ‘[’ Types ‘]’

A parameterized type T [U1,..., Un] consists of a type designator T and type parameters U ,..., U where n 1. T must refer to a type constructor which takes n type 1 n ≥ parameters a1,..., an with lower bounds L1,..., Ln and upper bounds U1,..., Un. The parameterized type is well-formed if each actual type parameter conforms to its bounds, i.e. L σ : T : U σ where σ is the substitution [a : T ,..., a : T ]. i < i < i 1 = 1 n = n

Example 3.2.2 Given the partial type deﬁnitions:

class TreeMap[a <: Ord[a], b] { ... } class List[a] { ... } class I extends Ord[I] { ... } 18 Types the following parameterized types are well formed:

TreeMap[I, String] List[I] List[List[Boolean]]

Example 3.2.3 Given the type deﬁnitions of Example 3.2.2, the following types are ill-formed:

TreeMap[I] // illegal: wrong number of parameters TreeMap[List[I], Boolean] // illegal: type parameter not within bound

3.2.5 Compound Types

Syntax:

Type ::= SimpleType {with SimpleType} [Refinement] Refinement ::= ‘{’ [RefineStat {‘;’ RefineStat}] ‘}’ RefineStat ::= Dcl | type TypeDef |

A compound type T1 with ... with Tn {R } represents objects with members as given in the component types T1,..., Tn and the refinement {R }. Each component type Ti must be a class type . A refinement {R } contains declarations and type definitions. Each declaration or definition in a refinement must override a declaration or definition in one of the component types T1,..., Tn. The usual rules for overriding (§5.1.5) apply. If no refinement is given, the empty refinement is implicitly added, i.e. T1 with ... with Tn is a shorthand for T1 with ... with Tn {}.

3.2.6 Function Types

Syntax:

SimpleType ::= Type1 ‘=>’ Type | ‘(’ [Types] ‘)’ ‘=>’ Type

The type (T1,..., Tn) => U represents the set of function values that take arguments of types T1,..., Tn and yield results of type U. In the case of exactly one argument type T => U is a shorthand for (T ) => U. Function types associate to the right, e.g. (S ) => (T ) => U is the same as (S ) => ((T ) => U ). Function types are shorthands for class types that deﬁne apply functions. Specif- ically, the n-ary function type (T1,..., Tn) => U is a shorthand for the class type Functionn[T1,..., Tn,U ]. Such class types are deﬁned in the Scala library for n between 0 and 9 as follows. 3.3 Non-Value Types 19

package scala; trait Functionn[-T1,..., -Tn, +R]{ def apply(x1: T1,..., xn: Tn): R; override def toString() = ""; }

Hence, function types are covariant in their result type, and contravariant in their argument types.

3.3 Non-Value Types

The types explained in the following do not denote sets of values, nor do they appear explicitly in programs. They are introduced in this report as the internal types of deﬁned identiﬁers.

3.3.1 Method Types

A method type is denoted internally as (Ts)U, where (Ts) is a sequence of types (T ,..., T ) for some n 0 and U is a (value or method) type. This type represents 1 n ≥ named methods that take arguments of types T1,..., Tn and that return a result of type U.

Method types associate to the right: (Ts1)(Ts2)U is treated as (Ts1)((Ts2)U). A special case are types of methods without any parameters. They are written here => T. Parameterless methods name expressions that are re-evaluated each time the parameterless method name is referenced. Method types do not exist as types of values. If a method name is used as a value, its type is implicitly converted to a corresponding function type (§3.7).

Example 3.3.1 The declarations

def a: Int def b (x: Int): Boolean def c (x: Int) (y: String, z: String): String produce the typings

a: => Int b: (Int) Boolean c: (Int) (String, String) String

3.3.2 Polymorphic Method Types

A polymorphic method type is denoted internally as [tps]T where [tps] is a type parameter section [a >: L <: U ,..., a >: L <: U ] for some n 0 and T 1 1 1 n n n ≥ 20 Types is a (value or method) type. This type represents named methods that take type arguments S1,..., Sn which conform (§3.2.4) to the lower bounds L1,..., Ln and the upper bounds U1,..., Un and that yield results of type T .

Example 3.3.2 The declarations

def empty[a]: List[a] def union[a <: Comparable[a]] (x: Set[a], xs: Set[a]): Set[a] produce the typings

empty : [a >: All <: Any] List[a] union : [a >: All <: Comparable[a]] (x: Set[a], xs: Set[a]) Set[a] .

3.4 Base Classes and Member Deﬁnitions

Types, bounds and base classes of class members depend on the way the members are referenced. Central here are three notions, namely:

1. the notion of the set of base classes of a type T , 2. the notion of a type T in some class C seen from some preﬁx type S, 3. the notion of a member binding of some type T .

These notions are deﬁned mutually recursively as follows. 1. The set of base classes of a type is a set of class types, given as follows.

• The base classes of a class type C are the base classes of class C. • The base classes of an aliased type are the base classes of its alias. • The base classes of an abstract type are the base classes of its upper bound.

• The base classes of a parameterized type C [T1,..., Tn] are the base classes of type C, where every occurrence of a type parameter ai of C has been replaced by the corresponding parameter type Ti . • The base classes of a singleton type p.type are the base classes of the type of p.

• The base classes of a compound type T1 with ... with Tn {R } are the reduced union of the base classes of all Ti ’s. This means: Let the multi-set S be the multi-set-union of the base classes of all Ti ’s. If S contains several type instances of the same class, say Si #C [T i ,..., T i ] (i I), then all those 1 n ∈ instances are replaced by one of them which conforms to all others. It is an error if no such instance exists, or if C is not a trait (§5.3). It follows that the reduced union, if it exists, produces a set of class types, where different types are instances of different classes. 3.4 Base Classes and Member Deﬁnitions 21

• The base classes of a type selection S#T are determined as follows. If T is an alias or abstract type, the previous clauses apply. Otherwise, T must be a (possibly parameterized) class type, which is deﬁned in some class B. Then the base classes of S#T are the base classes of T in B seen from the preﬁx type S.

2. The notion of a type T in class C seen from some prefix type S makes sense only if the prefix type S has a type instance of class C as a base class, say S0#C [T1,..., Tn]. Then we define as follows.

• If S = ².type, then T in C seen from S is T itself.

• Otherwise, if T is the i’th type parameter of some class D, then

– If S has a base class D[U1,..., Un], for some type parameters [U1,..., Un], then T in C seen from S is Ui .

– Otherwise, if C is deﬁned in a class C 0, then T in C seen from S is the same as T in C 0 seen from S0. – Otherwise, if C is not deﬁned in another class, then T in C seen from S is T itself.

• Otherwise, if T is the singleton type D.this.type for some class D then

– If D is a subclass of C and S has a type instance of class D among its base classes, then T in C seen from S is S.

• If T is some other type, then the described mapping is performed to all its type components.

If T is a possibly parameterized class type, where T ’s class is defined in some other class D, and S is some prefix type, then we use “T seen from S” as a shorthand for “T in D seen from S”. 3. The member bindings of a type T are all bindings d such that there exists a type instance of some class C among the base classes of T and there exists a definition or declaration d0 in C such that d results from d0 by replacing every type T 0 in d0 by T 0 in C seen from T . The definition of a type projection S#t is the member binding d of the type t in S. In that case, we also say that S#t is defined by d. 22 Types

3.5 Relations between types

We deﬁne two relations between types.

Type equivalence T UT and U are interchangeable in all contexts. ≡ Conformance T : U Type T conforms to type U. < 3.5.1 Type Equivalence

Equivalence ( ) between types is the smallest congruence2 such that the following ≡ holds:

• If t is defined by a type alias type t = T , then t is equivalent to T . • If a path p has a singleton type q.type, then p.type q.type. ≡ • If O is defined by an object definition, and p is a path consisting only of package or object selectors and ending in O, then O.this.type p.type. ≡ • Two compound types are equivalent if their component types are pairwise equivalent and their refinements are equivalent. Two refinements are equivalent if they bind the same names and the modifiers, types and bounds of every declared entity are equivalent in both refinements. • Two method types are equivalent if they have equivalent result types, both have the same number of parameters, and corresponding parameters have equivalent types as well as the same def or * modifiers. Note that the names of parameters do not matter for method type equivalence. • Two polymorphic types are equivalent if they have the same number of type parameters, and, after renaming one set of type parameters by another, the result types as well as lower and upper bounds of corresponding type parameters are equivalent. • Two overloaded types are equivalent if for every alternative type in either type there exists an equivalent alternative type in the other.

3.5.2 Conformance

The conformance relation ( :) is the smallest transitive relation that satisﬁes the < following conditions.

• Conformance includes equivalence. If T U then T : U. ≡ < • For every value type T , scala.All : T : scala.Any. < < • For every value type T : scala.AnyRef one has scala.AllRef : T . < <

2 A congruence is an equivalence relation which is closed under formation of contexts 3.5 Relations between types 23

• A type variable or abstract type t conforms to its upper bound and its lower bound conforms to t. • A class type or parameterized type c conforms to any of its base-types, b. • A type projection T #t conforms to U#t if T conforms to U.

• A parameterized type T [T1,..., Tn] conforms to T [U1,..., Un] if the following three conditions hold for i 1, ..., n. = – If the i’th type parameter of T is declared covariant, then T : U . i < i – If the i’th type parameter of T is declared contravariant, then U : T . i < i – If the i’th type parameter of T is declared neither covariant nor contravariant, then U T . i ≡ i

• A compound type T1 with ... with Tn {R } conforms to each of its component types Ti . • If T : U for i 1, ..., n and for every binding of a type or value x in R there < i = exists a member binding of x in T subsuming it, then T conforms to the compound type U1 with ... with Un {R }.

• If T T 0 for i 1, ..., n and U conforms to U0 then the method type i ≡ i = (T1,..., Tn)U conforms to (T10,..., Tn0 )U0.

• If, assuming L0 : a : U0 ,..., L0 : a : U0 one has L : L0 and U0 : U 1 < 1 < 1 n < n < n i < i i < i for i 1, ..., n, as well as T : T 0, then the polymorphic type [a : L : = < 1 > 1 < U ,..., a : L : U ]T conforms to the polymorphic type [a : L0 : 1 n > n < n 1 > 1 < U0 ,..., a : L0 : U0 ]T 0. 1 n > n < n • An overloaded type T and ... and T conforms to each of its alternative 1〈 〉 〈 〉 n types Ti . • A type S conforms to the overloaded type T and ... and T if S conforms to 1〈 〉 〈 〉 n each alternative type Ti .

A declaration or deﬁnition in some compound type of class type C subsumes another declaration of the same name in some compound type or class type C 0, if one of the following holds.

• A value declaration val x: T or value deﬁnition val x: T = e subsumes a value declaration val x: T 0 if T : T 0. < • A type alias type t T subsumes a type alias type t T 0 if T T 0. = = ≡ • A type declaration type t >: L <: U subsumes a type declaration type t >: L0 <: U0 if L0 : L and U : U0. < < • A type or class deﬁnition of some type t subsumes an abstract type declaration type t >: L <: U if L : t : U. < < The ( :) relation forms a partial order between types. The least upper bound or the < greatest lower bound of a set of types is understood to be relative to that order. 24 Types

Note. The least upper bound of a set of types does not always exist. For instance, consider the class deﬁnitions

class A[+t] {} class B extends A[B]; class C extends A[C];

Then the types A[Any], A[A[Any]], A[A[A[Any]]], ... form a descending sequence of upper bounds for B and C. The least upper bound would be the inﬁnite limit of that sequence, which does not exist as a Scala type. Since cases like this are in general impossible to detect, a Scala compiler is free to reject a term which has a type speciﬁed as a least upper or greatest lower bound, and that bound would be more complex than some compiler-set limit3.

3.6 Type Erasure

A type is called generic if it contains type arguments or type variables. Type erasure is a mapping from (possibly generic) types to non-generic types. We write T for | | the erasure of type T . The erasure mapping is deﬁned as follows.

• The erasure of a type variable is the erasure of its upper bound. • The erasure of a parameterized type T [T ,..., T ] is T . 1 n | | • The erasure of a singleton type p.type is the erasure of the type of p. • The erasure of a type projection T #x is |T |#x. • The erasure of a compound type T with ... with T {R } is T . 1 n | 1| • The erasure of every other type is the type itself.

3.7 Implicit Conversions

The following implicit conversions are applied to expressions of method type that are used as values, rather than being applied to some arguments.

• A parameterless method m of type => T is converted to type T by evaluating the expression to which m is bound. • An expression e of polymorphic type

[a1 >: L1 <: U1,..., an >: Ln <: Un]T

3The current Scala compiler limits the nesting level of parameterization in such bounds to 10. 3.7 Implicit Conversions 25

which does not appear as the function part of a type application is converted to type T by determining with local type inference (§10) instance types T1,..., Tn for the type variables a1,..., an and implicitly embedding e in the type application e[U1,..., Un] (§6.5). • An expression e of monomorphic method type (Ts )...(Ts )U of arity n 0 1 n > which does not appear as the function part of an application is converted to a function type by implicitly embedding e in the following term, where x is a fresh variable and each psi is a parameter section consisting of parameters with fresh names of types Tsi :

(val x = e ; (ps )...... (ps ) x(ps )...(ps )) 1 ⇒ ⇒ n ⇒ 1 n This conversion is not applicable to functions with call-by-name parameters x: => T or repeated parameters x: T*, (§4.5), because its result would violate the well-formedness rules for anonymous functions (§6.20). Hence, methods with such parameters always need to be applied to arguments immediately.

When used in an expression, a value of type byte, char, or short is always implicitly converted to a value of type int. Implicit conversions can also be user-deﬁned. This is expained in Chapter 8.

Chapter 4 Basic Declarations and Deﬁnitions

Syntax:

A declaration introduces names and assigns them types. It can appear as one of the statements of a class definition (§5.1) or as part of a refinement in a compound type (3.2.5). A definition introduces names that denote terms or types. It can form part of an object or class definition or it can be local to a block. Both declarations and definitions produce bindings that associate type names with type definitions or bounds, and that associate term names with types. The scope of a name introduced by a declaration or definition is the whole statement sequence containing the binding. However, there is a restriction on forward references: In a statement sequence s1 ...sn, if a simple name in si refers to an entity defined by s where j i, then every non-empty statement between and including j ≥ si and sj must be an import clause, or a function, type, class, or object definition. It may not be a value definition, a variable definition, or an expression. 28 Basic Declarations and Definitions

4.1 Value Declarations and Deﬁnitions

Syntax:

Dcl ::= val ValDcl ValDcl ::= id {‘,’ id} ‘:’ Type Def ::= val PatDef PatDef ::= Pattern2 {‘,’ Pattern2} [‘:’ Type] ‘=’ Expr

A value declaration val x: T introduces x as a name of a value of type T . A value definition val x: T = e defines x as a name of the value that results from the evaluation of e. The type T may be omitted, in which case the type of expression e is assumed. If a type T is given, then e is expected to conform to it. Evaluation of the value definition implies evaluation of its right-hand side e. The effect of the value definition is to bind x to the value of e converted to type T . Value definitions can alternatively have a pattern (§7.1) as left-hand side. If p is some pattern other than a simple name or a name followed by a colon and a type, then the value definition val p = e is expanded as follows: 1. If the pattern p has bound variables x ,..., x , where n 1: 1 n > val $x = e match {case p => scala.Tuplen(x1,..., xn)} val x1 = $x._1 ... val xn = $x._n .

Here, $x is a fresh name. The class Tuplen is deﬁned for n 2, ..., 9 in package = scala. 2. If p has a unique bound variable x:

val x = e match { case p => x }

3. If p has no bound variables:

e match { case p => ()}

Example 4.1.1 The following are examples of value deﬁnitions

val pi = 3.1415; val pi: double = 3.1415; // equivalent to first definition val Some(x) = f(); // a pattern definition val x :: xs = mylist; // an infix pattern definition

The last two deﬁnitions have the following expansions.

val x = f() match { case Some(x) => x } 4.2 Variable Declarations and Deﬁnitions 29

val x$ = mylist match { case x :: xs => scala.Tuple2(x, xs) } val x = x$._1; val xs = x$._2;

A value declaration val x1,..., xn: T is a shorthand for the sequence of value declarations val x1: T ; ...; val xn: T . A value definition val p1,..., pn = e is a shorthand for the sequence of value definitions val p1 = e; ...; val pn = e. A value definition val p1,..., pn : T = e is a shorthand for the sequence of value definitions val p1 : T = e; ...; val pn : T = e.

4.2 Variable Declarations and Deﬁnitions

Syntax:

Dcl ::= var VarDcl Def ::= var VarDef VarDcl ::= id {‘,’ id} ‘:’ Type VarDef ::= id {‘,’ id} [‘:’ Type] ‘=’ Expr | id {‘,’ id} ‘:’ Type ‘=’ ‘_’

A variable declaration var x: T is equivalent to declarations of a getter function x and a setter function x_=, deﬁned as follows:

def x: T ; def x_= (y: T ): unit

An implementation of a class containing variable declarations may define these variables using variable definitions, or it may define setter and getter functions directly. A variable definition var x: T = e introduces a mutable variable with type T and initial value as given by the expression e. The type T can be omitted, in which case the type of e is assumed. If T is given, then e is expected to conform to it. A variable definition var x: T = _ introduces a mutable variable with type T and a default initial value. The default value depends on the type T as follows:

0 if T is int or one of its subrange types, 0L if T is long, 0.0f if T is float, 0.0d if T is double, false if T is boolean, () if T is unit, null for all other types T .

When they occur as members of a template, both forms of variable deﬁnition also 30 Basic Declarations and Deﬁnitions introduce a getter function x which returns the value currently assigned to the variable, as well as a setter function x_= which changes the value currently assigned to the variable. The functions have the same signatures as for a variable declaration. The getter and setter functions are then members of the template instead of the variable accessed by them.

Example 4.2.1 The following example shows how properties can be simulated in Scala. It defines a class TimeOfDayVar of time values with updatable integer fields representing hours, minutes, and seconds. Its implementation contains tests that allow only legal values to be assigned to these fields. The user code, on the other hand, accesses these fields just like normal variables.

class TimeOfDayVar { private var h: int = 0; private var m: int = 0; private var s: int = 0;

def hours = h; def hours_= (h: int) = if (0 <= h && h < 24) this.h = h else throw new DateError();

def minutes = m; def minutes_= (m: int) = if (0 <= m && m < 60) this.m = m else throw new DateError();

def seconds = s; def seconds_= (s: int) = if (0 <= s && s < 60) this.s = s else throw new DateError(); } val d = new TimeOfDayVar; d.hours = 8; d.minutes = 30; d.seconds = 0; d.hours = 25; // throws a DateError exception

A variable declaration var x1,..., xn: T is a shorthand for the sequence of variable declarations var x1: T ; ...; var xn: T . A variable definition var x1,..., xn = e is a shorthand for the sequence of variable definitions var x1 = e; ...; var xn = e. A variable definition var x1,..., xn : T = e is a shorthand for the sequence of variable definitions var x1 : T = e; ...; var xn : T = e.

4.3 Type Declarations and Type Aliases

Syntax:

Dcl ::= type TypeDcl 4.3 Type Declarations and Type Aliases 31

TypeDcl ::= id [>: Type] [<: Type] Def ::= type TypeDef TypeDef ::= id [TypeParamClause] ‘=’ Type

A type declaration type t >: L <: U declares t to be an abstract type with lower bound type L and upper bound type U. If such a declaration appears as a member declaration of a type, implementations of the type may implement t with any type T for which L : T : U. Either or both bounds may be omitted. If the lower bound L < < is missing, the bottom type scala.All is assumed. If the upper bound U is missing, the top type scala.Any is assumed. A type alias type t = T defines t to be an alias name for the type T . The left hand side of a type alias may have a type parameter clause, e.g. type t [tps] = T . The scope of a type parameter extends over the right hand side T and the type parameter clause tps itself. The scope rules for definitions (§4) and type parameters (§4.5) make it possible that a type name appears in its own bound or in its right-hand side. However, it is a static error if a type alias refers recursively to the defined type constructor itself. That is, the type T in a type alias type t [tps] = T may not refer directly or indirectly to the name t. It is also an error if an abstract type is directly or indirectly its own upper or lower bound.

Example 4.3.1 The following are legal type declarations and deﬁnitions:

type IntList = List[Integer]; type T <: Comparable[T]; type Two[a] = Tuple2[a, a];

The following are illegal:

type Abs = Comparable[Abs]; // recursive type alias

type S <: T; // S, T are bounded by themselves. type T <: S;

type T <: AnyRef with T; // T is abstract, may not be part of // compound type

type T >: Comparable[T.That]; // Cannot select from T. // T is a type, not a value

If a type alias type t [tps] = S refers to a class type S, the name t can also be used as a constructor for objects of type S.

Example 4.3.2 The Predef module contains a deﬁnition which establishes Pair as an alias of the parameterized class Tuple2: 32 Basic Declarations and Deﬁnitions

type Pair[+a, +b] = Tuple2[a, b];

As a consequence, for any two types S and T , the type Pair[S, T ] is equivalent to the type Tuple2[S, T ]. Pair can also be used as a constructor instead of Tuple2, as in

new Pair[Int, Int](1, 2) .

4.4 Type Parameters

Syntax:

TypeParamClause ::= ‘[’ VarTypeParam {‘,’ VarTypeParam} ‘]’ VarTypeParam ::= [‘+’ | ‘-’] TypeParam TypeParam ::= id [>: Type] [<: Type | <% Type]

Type parameters appear in type definitions, class definitions, and function definitions. In this section we consider only type parameter definitions with lower bounds >: L and upper bounds <: U whereas a discussion of view bounds <% U are de- ferred to Section 8.4. The most general form of a type parameter is t >: L <: U. Here, L, and U are ± lower and upper bounds that constrain possible type arguments for the parameter, and is a variance, i.e. an optional prefix of either +, or -. ± The names of all type parameters in a type parameter clause must be pairwise different. The scope of a type parameter includes in each case the whole type parameter clause. Therefore it is possible that a type parameter appears as part of its own bounds or the bounds of other type parameters in the same clause. However, a type parameter may not be bounded directly or indirectly by itself.

Example 4.4.1 Here are some well-formed type parameter clauses:

[s, t] [ex <: Throwable] [a <: Ord[b], b <: a] [a, b, c >: a <: b]

The following type parameter clauses are illegal since type parameter are bounded by themselves.

[a >: a] [a <: b, b <: c, c <: a]

Variance annotations indicate how type instances with the given type parameters vary with respect to subtyping (§3.5.2). A ‘+’ variance indicates a covariant depen- 4.4 Type Parameters 33 dency, a ‘-’ variance indicates a contravariant dependency, and a missing variance indication indicates an invariant dependency. A variance annotation constrains the way the annotated type variable may appear in the type or class which binds the type parameter. In a type definition type t [tps] = S, type parameters labeled ‘+’ must only appear in covariant position in S whereas type parameters labeled ‘-’ must only appear in contravariant position. Analogously, for a class definition class c[tps](ps ): s extends t, type parameters labeled ‘+’ must only appear in covariant position in the self type s and the template t, whereas type parameters labeled ‘-’ must only appear in contravariant position. The variance position of a type parameter in a type or template is defined as follows. Let the opposite of covariance be contravariance, and the opposite of invariance be itself. The top-level of the type or template is always in covariant position. The variance position changes at the following constructs.

• The variance position of a method parameter is the opposite of the variance position of the enclosing parameter clause. • The variance position of a type parameter is the opposite of the variance position of the enclosing type parameter clause. • The variance position of the lower bound of a type declaration or type parameter is the opposite of the variance position of the type declaration or parameter. • The right hand side S of a type alias type t [tps] = S is always in invariant position. • The type of a mutable variable is always in invariant position. • The preﬁx S of a type selection S#T is always in invariant position. • For a type argument T of a type S[...T ... ]: If the corresponding type parameter is invariant, then T is in invariant position. If the corresponding type parameter is contravariant, the variance position of T is the opposite of the variance position of the enclosing type S[...T ... ].

Example 4.4.2 The following variance annotation is legal.

abstract class P[+a, +b] { def fst: a; def snd: b }

With this variance annotation, elements of type P subtype covariantly with respect to their arguments. For instance,

P[IOException, String] <: P[Throwable, AnyRef] .

If we make the elements of P mutable, the variance annotation becomes illegal. 34 Basic Declarations and Deﬁnitions

abstract class Q[+a, +b] { var fst: a; // **** error: illegal variance: var snd: b // ‘a’, ‘b’ occur in invariant position. }

Example 4.4.3 The following variance annotation is illegal, since a appears in contravariant position in the parameter of append:

trait Vector[+a] { def append(x: Vector[a]): Vector[a]; // **** error: illegal variance: // ‘a’ occurs in contravariant position. }

The problem can be avoided by generalizing the type of append by means of a lower bound:

trait Vector[+a] { def append[b >: a](x: Vector[b]): Vector[b]; }

Example 4.4.4 Here is a case where a contravariant type parameter is useful.

trait OutputChannel[-a] { def write(x: a): unit }

With that annotation, we have that OutputChannel[AnyRef] conforms to OutputChannel[String]. That is, a channel on which one can write any object can substitute for a channel on which one can write only strings.

4.5 Function Declarations and Deﬁnitions

Syntax:

Dcl ::= def FunDcl FunDcl ::= FunSig {‘,’ FunSig} ‘:’ Type Def ::= def FunDef FunDef ::= FunSig {‘,’ FunSig} [‘:’ Type] ‘=’ Expr FunSig ::= id [FunTypeParamClause] {ParamClause} FunTypeParamClause ::= ‘[’ TypeParam {‘,’ TypeParam} ‘]’ ParamClause ::= ‘(’ [Param {‘,’ Param}] ‘)’ Param ::= id ‘:’ [‘=>’] Type [‘*’] 4.5 Function Declarations and Deﬁnitions 35

A function declaration has the form def f psig: T , where f is the function’s name, psig is its parameter signature and T is its result type. A function definition f psig: T = e also includes a function body e, i.e. an expression which defines the function’s result. A parameter signature consists of an optional type parameter clause [tps], followed by zero or more value parameter clauses (ps1)...(psn). Such a declaration or definition introduces a value with a (possibly polymorphic) method type whose parameter types and result type are as given. A type parameter clause tps consists of one or more type declarations (§4.3), which introduce type parameters, possibly with bounds. The scope of a type parameter includes the whole signature, including any of the type parameter bounds as well as the function body, if it is present. A value parameter clause ps consists of zero or more formal parameter bindings such as x: T , which bind value parameters and associate them with their types. The scope of a formal value parameter name x is the function body, if one is given. Both type parameter names and value parameter names must be pairwise distinct. The type of a value parameter may be prefixed by =>, e.g. x: => T . The type of such a parameter is then the parameterless method type => T . This indicates that the corresponding argument is not evaluated at the point of function application, but instead is evaluated at each use within the function. That is, the argument is evaluated using call-by-name.

Example 4.5.1 The declaration

def whileLoop (cond: => Boolean) (stat: => Unit): Unit indicates that both parameters of whileLoop are evaluated using call-by-name.

The last value parameter of a parameter section may be sufﬁxed by “*”, e.g. (..., x:T *). The type of such a repeated parameter inside the method is then the sequence type scala.Seq[T ]. Methods with repeated parameters T * take a variable number of arguments of type T . That is, if a method m with type (T ,..., T ,S*)U is applied to arguments (e ,..., e ) where k n, then m is taken 1 n 1 k ≥ in that application to have type (T ,..., T ,S,..., S)U, with k n occurrences of type 1 n − S.

Example 4.5.2 The following method deﬁnition computes the sum of a variable number of integer arguments.

def sum(args: int*){ var result = 0; for (val arg <- args.elements) result = result + arg; result }

The following applications of this method yield 0, 1, 6, in that order. 36 Basic Declarations and Deﬁnitions

sum() sum(1) sum(1, 2, 3, 4, 5)

The type of the function body must conform to the function’s declared result type, if one is given. If the function deﬁnition is not recursive, the result type may be omitted, in which case it is determined from the type of the function body.

For any index i let fsigi be a function signature consisting of a function name, an optional type parameter section, and zero or more parameter sections. Then a function declaration def fsig1,..., fsign: T is a shorthand for the sequence of function declarations def fsig1: T ; ...; def fsign: T .A function definition def fsig1,..., fsign = e is a shorthand for the sequence of function definitions def fsig1 = e; ...; def fsign = e. A function definition def fsig1,..., fsign : T = e is a shorthand for the sequence of function definitions def fsig1 : T = e; ...; def fsign : T = e.

4.6 Overloaded Deﬁnitions

An overloaded definition is a set of n 1 value or function definitions in the same > statement sequence that define the same name, binding it to types T1,..., Tn, respectively. The individual definitions are called alternatives. Overloaded definitions may only appear in the statement sequence of a template. Alternatives always need to specify the type of the defined entity completely. It is an error if the types of two alternatives Ti and Tj have the same erasure (§3.6).

4.7 Import Clauses

Syntax:

Import ::= import ImportExpr {‘,’ ImportExpr} ImportExpr ::= StableId ‘.’ (id | ‘_’ | ImportSelectors) ImportSelectors ::= ‘{’ {ImportSelector ‘,’} (ImportSelector | ‘_’) ‘}’ ImportSelector ::= id [‘=>’ id | ‘=>’ ‘_’]

An import clause has the form import p.I where p is a stable identiﬁer (§3.1) and I is an import expression. The import expression determines a set of names of members of p which are made available without qualiﬁcation. The most general form of an import expression is a list of import selectors

{ x1 => y1,..., xn => yn,_} 4.7 Import Clauses 37 for n 0, where the final wildcard ‘_’ may be absent. It makes available each mem- ≥ ber p.xi under the unqualified name yi . I.e. every import selector xi => yi renames p.xi to yi . If a final wildcard is present, all members z of p other than x1,..., xn are also made available under their own unqualified names. Import selectors work in the same way for type and term members. For instance, an import clause import p.{x => y } renames the term name p.x to the term name y and the type name p.x to the type name y. At least one of these two names must reference a member of p. If the target in an import selector is a wildcard, the import selector hides access to the source member. For instance, the import selector x => _ “renames” x to the wildcard symbol (which is unaccessible as a name in user programs), and thereby effectively prevents unqualified access to x. This is useful if there is a final wildcard in the same import selector list, which imports all members not mentioned in previous import selectors. Several shorthands exist. An import selector may be just a simple name x. In this case, x is imported without renaming, so the import selector is equivalent to x => x. Furthermore, it is possible to replace the whole import selector list by a single identifier or wildcard. The import clause import p.x is equivalent to import p.{x } , i.e. it makes available without qualification the member x of p. The import clause import p._ is equivalent to import p.{_}, i.e. it makes available without qualification all members of p (this is analogous to import p.* in Java).

An import clause with multiple import expressions import p1.I1,..., pn.In is interpreted as a sequence of import clauses import p1.I1; ...; import pn.In.

Example 4.7.1 Consider the object deﬁnition:

object M{ def z = 0, one = 1; def add(x: Int, y: Int): Int = x + y }

Then the block

{ import M.{one, z => zero, _}; add(zero, one) } is equivalent to the block

{ M.add(M.z, M.one) } .

Chapter 5 Classes and Objects

Syntax:

TmplDef ::= ([case] class | trait) ClassDef | [case] object ObjectDef

Classes (§5.2) and objects (§5.4) are both deﬁned in terms of templates.

5.1 Templates

Syntax:

Template ::= Constr {‘with’ Constr} [TemplateBody] TemplateBody ::= ‘{’ [TemplateStat {‘;’ TemplateStat}] ‘}’

A template defines the type signature, behavior and initial state of a class of objects or of a single object. Templates form part of instance creation expressions, class definitions, and object definitions. A template sc with mc1 with ... with mcn {stats} consists of a constructor invocation sc which defines the template’s superclass, constructor invocations mc ,..., mc (n 1 n ≥ 0), which define the template’s mixin classes, and a statement sequence stats which contains additional member definitions for the template. Superclass and mixin classes together are called the parent classes of a template. They must be pairwise different. The superclass of a template must be a subtype of the superclass of each mixin class. The least proper supertype of a template is the class type or compound type (§3.2.5) consisting of the its parent classes. Member definitions define new members or overwrite members in the parent classes. If the template forms part of a class definition, the statement part stats may also contain declarations of abstract members. 40 Classes and Objects

Inheriting from Java Types. A template may have a Java class as its superclass and Java interfaces as its mixin classes. On the other hand, it is not permitted to have a Java class as a mixin class, or a Java interface as a superclass.

5.1.1 Constructor Invocations

Syntax:

Constr ::= StableId [TypeArgs] [‘(’ [Exprs] ‘)’]

Constructor invocations define the type, members, and initial state of objects created by an instance creation expression, or of parts of an object’s definition which are inherited by a class or object definition. A constructor invocation is a function application x.c(args), where x is a stable identifier (§3.1), c is a type name which either designates a class or defines an alias type for one, and args is an argument list, which matches one of the constructors of that class. The prefix ‘x.’ can be omitted. The argument list (args) can also be omitted, in which case an empty argument list () is implicitly added.

5.1.2 Base Classes

For every template, class type and constructor invocation we deﬁne two sets of class types: the base classes and mixin base classes. Their deﬁnitions are as follows.

The mixin base classes of a template sc with mc1 with ... with mcn {stats} are the reduced union (§3.4) of the base classes of all mixins mci . The mixin base classes of a class type C are the mixin base classes of the template augmented by C itself. The mixin base classes of a constructor invocation of type T are the mixin base classes of class T . The base classes of a template consist are the reduced union of the base classes of its superclass and the template’s mixin base classes. The base classes of class scala.Any consist of just the class itself. The base classes of some other class type C are the base classes of the template represented by C augmented by C itself. The base classes of a constructor invocation of type T are the base classes of T . The notions of mixin base classes and base classes are extended from classes to arbitrary types following the deﬁnitions of §3.4.

Example 5.1.1 Consider the following class deﬁnitions:

class A; class B extends A; trait C extends A; class D extends A; class E extends B with C with D; class F extends B with D with E; 5.1 Templates 41

The mixin base classes and base classes of classes A-F are given in the following table:

Mixin base classes Base classes A A A, ScalaObject, AnyRef, Any B B B, A, ScalaObject, AnyRef, Any C C C, A, ScalaObject, AnyRef, Any D D D, A, ScalaObject, AnyRef, Any E C, D, E E, B, C, D, A, ScalaObject, AnyRef, Any F C, D, E, F F,B, D, E, C, A, ScalaObject, AnyRef, Any

Note that D is inherited twice by F, once directly, the other time indirectly through E. This is permitted, since D is a trait.

5.1.3 Evaluation

The evaluation of a template or constructor invocation depends on whether the template defines an object or is a superclass of a constructed object, or whether it is used as a mixin for a defined object. In the second case, the evaluation of a template used as a mixin depends on an actual superclass, which is known at the point where the template is used in a definition of an object, but not at the point where it is defined. The actual superclass is used in the determination of the meaning of super (§6.3). We therefore define two notions of template evaluation: (Plain) evaluation (as a defining template or superclass) and mixin evaluation with a given superclass sc. These notions are defined for templates and constructor invocations as follows. A mixin evaluation with superclass sc of a template sc0 with mc1 with mcn {stats} consists of mixin evaluations with superclass sc of the mixin constructor invocations mc1,..., mcn in the order they are given, followed by an evaluation of the statement sequence stats. Within stats the actual superclass refers to sc. A mixin evaluation with superclass sc of a class constructor invocation ci consists of an evaluation of the constructor function and its arguments in the order they are given, followed by a mixin evaluation with superclass sc of the template represented by the constructor invocation.

An evaluation of a template sc with mc1 with mcn with (stats) consists of an evaluation of the superclass constructor invocation sc, followed by a mixin evaluation with superclass sc of the template. An evaluation of a class constructor invocation ci consists of an evaluation of the constructor function and its arguments in the order they are given, followed by an evaluation of the template represented by the constructor invocation. 42 Classes and Objects

5.1.4 Template Members

The object resulting from evaluation of a template has directly bound members and inherited members. Members can be abstract or concrete. For a template T these categories are deﬁned as follows.

1. A directly bound member of T is an entity introduced by a member deﬁnition or declaration in T ’s statement sequence. The member is called abstract if it is introduced by a declaration, concrete otherwise. 2. A concrete inherited member of T is a non-private, concrete member of one of T ’s parent classes, except if a member with the same name is already directly bound in T or the member is mixin-overridden in T . A member m of T ’s superclass is mixin-overridden in T if there is a concrete member of a mixin base class of T which either overrides m itself or overrides a member named m of a base class of T ’s superclass. 3. An abstract inherited member of T is a non-private, abstract member of one of T ’s parent classes Pi , except if the template has a directly bound or concrete inherited member with the same name, or the template has an abstract member inherited from a parent class P where j i. j > It is an error if a template has more than one member with the same name.

Example 5.1.2 Consider the class deﬁnitions

class A{ def f: Int = 1 ; def g: Int = 2 ; def h: Int = 3 } abstract class B{ def f: Int = 4 ; def g: Int } abstract class C extends A with B{ def h: Int }

Then class C has a directly bound abstract member h. It inherits member f from class B and member g from class A.

5.1.5 Overriding

A template member M that has the same name as a non-private member M0 of a base class (and that belongs to the same namespace) is said to override that member. In this case the binding of the overriding member M must subsume (§3.5.2) the binding of the overridden member M0. Furthermore, the overridden definition may not be a class definition. Method definitions may only override other method definitions (or the methods implicitly defined by a variable definition). They may not override value definitions. Finally, the following restrictions on modifiers apply to M and M0:

• M0 must not be labeled final. • M must not be labeled private. 5.1 Templates 43

• If M is labeled protected, then M0 must also be labeled protected.

• If M0 is not an abstract member, then M must be labeled override.

• If M0 is labeled abstract and override, and M0 is a member of the static superclass of the class containing the deﬁnition of M, then M must also be labeled abstract and override.

Example 5.1.3 Consider the deﬁnitions:

trait Root { type T <: Root } trait A extends Root { type T <: A } trait B extends Root { type T <: B } trait C extends A with B;

Then the trait deﬁnition C is not well-formed because the binding of T in C is type T <: B, which fails to subsume the binding type T <: A of T in type A. The problem can be solved by adding an overriding deﬁnition of type T in class C:

class C extends A with B{ type T <: C }

5.1.6 Modiﬁers

Syntax:

Member definitions may be preceded by modifiers which affect the accessibility and usage of the identifiers bound by them. If several modifiers are given, their order does not matter, but the same modifier may not occur repeatedly. Modifiers preceding a repeated definition apply to all constituent definitions. The rules gov- erning the validity and meaning of a modifier are as follows.

• The private modifier can be used with any definition in a template. Private members can be accessed only from within the template that defines them. Private members are not inherited by subclasses and they may not override definitions in parent classes. private may not be applied to abstract members, and it may not be combined in one modifier list with protected, final or override. • The protected modifier applies to class member definitions. Protected members can be accessed from within the template of the defining class as well as 44 Classes and Objects

in all templates that have the deﬁning class as a base class. A protected iden- tiﬁer x may be used as a member name in a selection r.x only if r is one of the reserved words this and super, or if r’s type conforms to a type-instance of the class which contains the access.

• The override modifier applies to class member definitions. It is mandatory for member definitions that override some other concrete member definition in a super- or mixin-class. If an override modifier is given, there must be at least one overridden member definition. The override modifier has an additional significance when combined with the abstract modifier. That modifier combination is only allowed for members of abstract classes. A member labeled abstract and override must override some member of the superclass of the class containing the definition. We call a member of a template incomplete if it is either abstract (i.e. defined by a declaration), or it is labeled abstract and override and it overrides an incomplete member of the template’s superclass. Note that the abstract override modifier combination does not influence the concept whether a member is concrete or abstract. A member for which only a declaration is given is abstract, whereas a member for which a full definition is given is concrete.

• The abstract modifier is used in class definitions. It is mandatory if the class has incomplete members. Abstract classes cannot be instantiated (§6.7) with a constructor invocation unless followed by mixin constructors or statements which override all incomplete members of the class. The abstract modifier can also be used in conjunction with override for class member definitions. In that case the meaning of the previous discussion applies.

• The final modifier applies to class member definitions and to class definitions. A final class member definition may not be overridden in subclasses. A final class may not be inherited by a template. final is redundant for object definitions. Members of final classes or objects are implicitly also final, so the final modifier is redundant for them, too. final may not be applied to incomplete members, and it may not be combined in one modifier list with private or sealed.

• The sealed modiﬁer applies to class deﬁnitions. A sealed class may not be inherited, except if either

– the inheriting template is nested within the definition of the sealed class itself, or – the inheriting template belongs to a class or object definition which forms part of the same statement sequence as the definition of the sealed class. 5.1 Templates 45

Example 5.1.4 A useful idiom to prevent clients of a class from constructing new instances of that class is to declare the class abstract and sealed:

object m { abstract sealed class C (x: Int) { def nextC = C(x + 1) {} } val empty = new C(0) {} }

For instance, in the code above clients can create instances of class m.C only by call- ing the nextC method of an existing m.C object; it is not possible for clients to create objects of class m.C directly. Indeed the following two lines are both in error:

m.C(0) // **** error: C is abstract, so it cannot be instantiated. m.C(0) {} // **** error: illegal inheritance from sealed class.

5.1.7 Attributes

Syntax:

AttributeClause ::= ‘[’ Attribute {‘,’ Attribute} ‘]’ Attribute ::= Constr

Attributes associate meta-information with definitions. A simple attribute clause has the form [C] or [C(a1,..., an)]. Here, c is a constructor of a class C, which must comform to the class scala.Attribute. All given constructor arguments a1,..., an must be constant expressions. An attribute clause applies to the first definition or declaration following it. More than one attribute clause may precede a definition and declaration. The order in which these clauses are given does not matter. It is also possible to combine several attributres separated by commas in one clause. Such a combined clause [A1,..., An] is equivalent to a set of clauses [A1]...[An]. The meaning of attribute clauses is implementation-dependent. On the Java plat- form, the following attributes have a standard meaning.

transient

Marks a ﬁeld to be non-persistent; this is equivalent to the transient modiﬁer in Java. volatile

Marks a ﬁeld which can change its value outside the control of the program; this is equivalent to the volatile modiﬁer in Java.

Serializable 46 Classes and Objects

Marks a class to be serializable; this is equivalent to inheriting from the java.io.Serializable interface in Java.

SerialVersionUID()

Attaches a serial version identifier (a long constant) to a class. This is equivalent to a the following field definition in Java:

private final static SerialVersionUID = ;

5.2 Class Deﬁnitions

Syntax:

TmplDef ::= class ClassDef ClassDef ::= ClassSig {‘,’ ClassSig} [‘:’ SimpleType] ClassTemplate ClassSig ::= id [TypeParamClause] [ClassParamClause] ClassTemplate ::= extends Template | TemplateBody | ClassParamClause ::= ‘(’ [ClassParam {‘,’ ClassParam}] ‘)’ ClassParam ::= [{Modifier} ‘val’] Param

The most general form of class deﬁnition is class c[tps](ps ): s extends t. Here,

c is the name of the class to be deﬁned.

tps is a non-empty list of type parameters of the class being defined. The scope of a type parameter is the whole class definition including the type parameter section itself. It is illegal to define two type parameters with the same name. The type parameter section [tps] may be omitted. A class with a type parameter section is called polymorphic, otherwise it is called monomorphic.

ps is a formal value parameter clause for the primary constructor of the class. The scope of a formal value parameter includes the template t. However, a formal value parameter may not form part of the types of any of the parent classes or members of t. It is illegal to deﬁne two formal value parameters with the same name. The formal parameter section (ps ) may be omitted, in which case an empty parameter section () is assumed.

If a formal parameter declaration x : T is preceded by a val keyword, an accessor definition for this parameter is implicitly added to the class. The accessor introduces a value member x of c that is defined as alias of the parameter. The formal paremter declaration may contain modifiers, which then carry over to the accessor definition. 5.2 Class Definitions 47

s is the self type of the class. Inside the class, the type of this is assumed to be s. The self type must conform to the self types of all classes which are inherited by the template t. The self type declaration ‘:s’ may be omitted, in which case the self type of the class is assumed to be equal to c[tps]. t is a template (§5.1) of the form

sc with mc with ... with mc { stats } (n 0) 1 n ≥ which deﬁnes the base classes, behavior and initial state of objects of the class. The extends clause extends sc can be omitted, in which case extends scala.AnyRef is assumed. The class body {stats} may also be omitted, in which case the empty body {} is assumed.

This class deﬁnition deﬁnes a type c[tps] and a constructor which when applied to parameters conforming to types ps initializes instances of type c[tps] by evaluating the template t.

For any index i let csigi be a class signature consisting of a class name and optional type parameter and value parameter sections. Let ct be a class template. Then a class definition class csig1,..., csign ct is a shorthand for the sequence of class definitions class csig1 ct ; ...; class csign ct. A class definition class csig1,..., csign : T ct is a shorthand for the sequence of class definitions class csig1 : T ct ; ...; class csign : T ct.

5.2.1 Constructor Deﬁnitions

Syntax:

FunDef ::= this ParamClause‘=’ ConstrExpr ConstrExpr ::= this ArgumentExprs | ‘{’ this ArgumentExprs {‘;’ BlockStat} ‘}’

A class may have additional constructors besides the primary constructor. These are defined by constructor definitions of the form def this(ps ) = e. Such a definition introduces an additional constructor for the enclosing class, with parameters as given in the formal parameter list ps, and whose evaluation is defined by the constructor expression e. The scope of each formal parameter is the constructor expression e. A constructor expression is either a self constructor invocation this(args) or a block which begins with a self constructor invocation. Neither the signature, nor the self constructor invocation of a constructor definition may refer to this, or refer to value parameters or members of the enclosing class by simple name. If there are auxiliary constructors of a class C, they define together with C’s primary constructor an overloaded constructor value. The usual rules for overloading resolution (§4.6) apply for constructor invocations of C, including the self constructor invocations in the constructor expressions themselves. To prevent infinite cycles 48 Classes and Objects of constructor invocations, there is the restriction that every self constructor invocation must refer to a constructor definition which precedes it (i.e. it must refer to either a preceding auxiliary constructor or the primary constructor of the class). The type of a constructor expression must be always so that a generic instance of the class is constructed. I.e., if the class in question has name C and type parameters [tps], then each constructor must construct an instance of C [tps]; it is not permitted to instantiate formal type parameters.

Example 5.2.1 Consider the class deﬁnition

class LinkedList[a]() { var head = _; var tail = null; def isEmpty = tail != null; def this(head: a) = { this(); this.head = head; } def this(head: a, tail: List[a]) = { this(head); this.tail = tail } }

This deﬁnes a class LinkedList with an overloaded constructor of type

[a](): LinkedList[a] and 〈 〉 [a](x: a): LinkedList[a] and 〈 〉 [a](x: a, xs: LinkedList[a]): LinkedList[a] .

The second constructor alternative constructs an singleton list, while the third one constructs a list with a given head and tail.

5.2.2 Case Classes

Syntax:

TmplDef ::= case class ClassDef

If a class definition is prefixed with case, the class is said to be a case class. The primary constructor of a case class may be used in a constructor pattern (§7.1). The following four restrictions ensure efficient pattern matching for case classes.

1. None of the base classes of a case class may be a case class.

2. No type may have two different case classes among its base types.

3. A case class may not inherit indirectly from a sealed class. That is, if a base class b of a case class c is marked sealed, then b must be a parent class of c.

4. The primary constructor of a case class may not have any call-by-name parameters (§4.5). 5.2 Class Deﬁnitions 49

A case class definition of c[tps](ps ) with type parameters tps and value parameters ps implicitly generates a function definition for a case class factory together with the class definition itself:

def c[tps](ps ): s = new c[tps](ps )

(Here, s is the self type of class c. If a type parameter section is missing in the class, it is also missing in the factory definition). All formal value parameters of a case class are implicitly prefixed with a val keyword. Therefore, accessor definitions (§5.2) for such parameters are generated. Also implicitly defined are accessor member definitions in the class that return its value parameters. Every binding x : T in the parameter section leads to a value definition of x that defines x to be an alias of the parameter. Every case class implicitly overrides some method definitions of class scala.AnyRef (§12.1) unless a definition of the same method is already given in the case class itself or a concrete definition of the same method is given in some base class of the case class different from AnyRef. In particular:

Method equals: (Any)boolean is structural equality, where two instances are equal if they belong to the same class and have equal (with respect to equals) primary constructor arguments. Method hashCode: ()int computes a hash-code depending on the data structure in a way which maps equal (with respect to equals) values to equal hash-codes. Method toString: ()String returns a string representation which contains the name of the class and its primary constructor arguments.

Example 5.2.2 Here is the deﬁnition of abstract syntax for lambda calculus:

class Expr; case class Var (x: String) extends Expr, Apply (f: Expr, e: Expr) extends Expr, Lambda (x: String, e: Expr) extends Expr;

This deﬁnes a class Expr with case classes Var, Apply and Lambda. A call-by-value evaluator for lambda expressions could then be written as follows.

type Env = String => Value; case class Value(e: Expr, env: Env);

def eval(e: Expr, env: Env): Value = e match { case Var (x) => env(x) 50 Classes and Objects

case Apply(f, g) => val Value(Lambda (x, e1), env1) = eval(f, env); val v = eval(g, env); eval (e1, (y => if (y == x) v else env1(y))) case Lambda(_, _) => Value(e, env) }

It is possible to deﬁne further case classes that extend type Expr in other parts of the program, for instance

case class Number(x: Int) extends Expr;

This form of extensibility can be excluded by declaring the base class Expr sealed; in this case, the only classes permitted to extend Expr are those which are nested inside Expr, or which appear in the same statement sequence as the deﬁnition of Expr.

5.3 Traits

Syntax:

TmplDef ::= trait ClassDef

A class definition which starts with the reserved word trait instead of class defines a trait. A trait is a specific kind of an abstract class, so the abstract modifier is redundant for it. The trait definition must satisfy the following four restrictions.

1. There are no value parameters in the trait’s primary constructor, nor are there secondary constructors. 2. All mixin base classes of the trait are traits. 3. All parent class constructors of the trait are primary constructors with empty value parameter lists. 4. All non-empty statements in the trait’s template are either imports or pure deﬁnitions.

A pure definition can be evaluated without any side effect. Function, type, class, or object definitions are always pure. A value definition is pure if its right-hand side expression is pure. A secondary constructor definition is pure if its right-hand side consists only Pure expressions are paths, literals, and typed expressions e : T where e is pure. These restrictions ensure that the evaluation of the mixin constructor of a trait has no effect. Therefore, traits may appear several times in the base classes of a template, whereas other classes cannot. 5.4 Object Definitions 51

Example 5.3.1 The following trait class deﬁnes the property of being ordered, i.e. comparable to objects of some type. It contains an abstract method < and default implementations of the other comparison operators <=, >, and >=.

trait Ord[t <: Ord[t]]: t { def < (that: t): Boolean; def <=(that: t): Boolean = this < that || this == that; def > (that: t): Boolean = that < this; def >=(that: t): Boolean = that <= this; }

5.4 Object Deﬁnitions

Syntax:

ObjectDef ::= id {‘,’ id} [‘:’ SimpleType] ClassTemplate

An object deﬁnition deﬁnes a single object of a new class. Its most general form is object m: s extends t. Here,

m is the name of the object to be defined. s is the self type of the object. References to m are assumed to have type s. Furthermore, inside the template t, the type of this is also assumed to be s. The type of the anonymous class defined by t must conform to s and s must conform to the self types of all classes which are inherited by t. The self type declaration ‘: s’ may be omitted, in which case the self type is assumed to be equal to the anonymous class defined by t. t is a template (§5.1) of the form

sc with mc1 with ... with mcn { stats }

which deﬁnes the base classes, behavior and initial state of m. The extends clause extends sc can be omitted, in which case extends scala.AnyRef is assumed. The class body {stats} may also be omitted, in which case the empty body {} is assumed.

The object definition defines a single object (or: module) conforming to the template t. It is roughly equivalent to a class definition and a value definition that cre- ates an object of the class:

final class m$cls: s extends t; final val m: s = new m$cls;

(The final modiﬁers are omitted if the deﬁnition occurs as part of a block. The class name m$cls is not accessible for user programs.) 52 Classes and Objects

There are however two differences between an object definition and a pair of class and value definitions such as the one given above. First, object definitions may appear as top-level definitions in a compilation unit, whereas value definitions may not. Second, the module defined by an object definition is instantiated lazily. The new m$cls constructor is evaluated not at the point of the object definition, but is instead evaluated the first time m is dereferenced during execution of the program (which might be never at all). An attempt to dereference m again in the course of evaluation of the constructor leads to a infinite loop or run-time error. Other threads trying to dereference m while the constructor is being evaluated block until evaluation is complete.

Example 5.4.1 Classes in Scala do not have static members; however, an equivalent effect can be achieved by an accompanying object deﬁnition E.g.

abstract class Point { val x: Double; val y: Double; def isOrigin = (x == 0.0 && y == 0.0); } object Point { val origin = new Point() { val x = 0.0; val y = 0.0 } }

This defines a class Point and an object Point which contains origin as a member. Note that the double use of the name Point is legal, since the class definition defines the name Point in the type name space, whereas the object definition defines a name in the term namespace. This technique is applied by the Scala compiler when interpreting a Java class with static members. Such a class C is conceptually seen as a pair of a Scala class that contains all instance members of C and a Scala object that contains all static members of C. Let ct be a class template. Then an object definition object x1,..., xn ct is a shorthand for the sequence of object definitions object x1 ct ; ...; object xn ct. An object definition object x1,..., xn : T ct is a shorthand for the sequence of object definitions object x1 : T ct ; ...; object xn : T ct. Chapter 6 Expressions

Syntax:

Expr ::= [Bindings ‘=>’] Expr | Expr1 Expr1 ::= if ‘(’ Expr ‘)’ Expr [[‘;’] else Expr] | try ‘{’ block ‘}’ [catch Expr] [finally Expr] | while ’(’ Expr ’)’ Expr | do Expr [‘;’] while ‘(’ Expr ’)’ | for ‘(’ Enumerators ‘)’ [yield] Expr | return [Expr] | throw Expr | [SimpleExpr ‘.’] id ‘=’ Expr | SimpleExpr ArgumentExprs ‘=’ Expr | PostfixExpr [‘:’ Type1] | MethodClosure PostfixExpr ::= InfixExpr [id] InfixExpr ::= PrefixExpr | InfixExpr id PrefixExpr PrefixExpr ::= [‘-’ | ‘+’ | ‘~’ | ‘!’] SimpleExpr SimpleExpr ::= Literal | Path | ‘(’ [Expr] ‘)’ | BlockExpr | new Template | SimpleExpr ‘.’ id | SimpleExpr TypeArgs | SimpleExpr ArgumentExprs | XmlExpr ArgumentExprs ::= ‘(’ [Exprs] ’)’ | BlockExpr MethodClosure ::= ‘.’ Id {‘.’ Id | TypeArgs | ArgumentExprs} 54 Expressions

BlockExpr ::= ‘{’ CaseClause {CaseClause} ‘}’ | ‘{’ Block ‘}’ Block ::= {BlockStat ‘;’} [ResultExpr] ResultExpr ::= Expr1 | Bindings ‘=>’ Block Exprs ::= Expr {‘,’ Expr}

Expressions are composed of operators and operands. Expression forms are dis- cussed subsequently in decreasing order of precedence. The typing of expressions is often relative to some expected type. When we write “expression e is expected to conform to type T ”, we mean: (1) the expected type of e is T , and (2) the type of expression e must conform to T .

6.1 Literals

Syntax:

Typing and evaluation of numeric, character, and string literals are generally as in Java. An integer literal denotes an integer number. Its type is normally int. How- ever, if the expected type pt of the expression is either byte, short, or char and the integer number fits in the numeric range defined by the type, then the number is converted to type pt and the expression’s type is pt. A floating point literal denotes a single-precision or double precision IEEE floating point number. A character literal denotes a Unicode character. A string literal denotes a member of String. A symbol literal ’x is a shorthand for the expression scala.Symbol("x"). If the symbol literal is followed by actual parameters, as in ’x(args), then the whole expression is taken to be a shorthand for scala.Symbol("x", args). The boolean truth values are denoted by the reserved words true and false. The type of these expressions is boolean, and their evaluation is immediate. The null literal is of type scala.AllRef. It denotes a reference value which refers to a special “null’ object, which implements methods in class scala.AnyRef as follows:

• eq(x ), ==(x ), equals(x ) return true iff their argument x is also the “null” 6.2 Designators 55

object. • isInstanceOf[T ] always returns false. • asInstanceOf[T ] returns the “null” object itself if T conforms to scala.AnyRef, and throws a NullPointerException otherwise. • toString() returns the string “null”.

A reference to any other member of the “null” object causes a NullPointerException to be thrown.

6.2 Designators

Syntax:

Designator ::= Path | SimpleExpr ‘.’ id

A designator refers to a named term. It can be a simple name or a selection. If r is a stable identifier of type T , the selection r.x refers to the term member of r that is identified in T by the name x. For other expressions e, e.x is typed as if it was (val y e ; y.x) for some fresh name y. The typing rules for blocks implies that in = that case x’s type may not refer to any abstract type member of e. The expected type of a designator’s prefix is always missing. The type of a designator is normally the type of the entity it refers to. However, if the designator is a path (§3.1) p, its type is p.type, provided the expression’s expected type is a singleton type, or p occurs as the prefix of a selection or type selection. The selection e.x is evaluated by first evaluating the qualifier expression e. The selection’s result is then the value to which the selector identifier is bound in the object resulting from evaluation of e.

6.3 This and Super

Syntax:

SimpleExpr ::= [id ‘.’] this | [id ‘.’] super [‘[’ id ‘]’] ‘.’ id

The expression this can appear in the statement part of a template or compound type. It stands for the object being deﬁned by the innermost template or compound type enclosing the reference. If this is a compound type, the type of this is that compound type. If it is a template of an instance creation expression, the type of this is the type of that template. If it is a template of a class or object deﬁnition with simple name C, the type of this is the same as the type of C .this. 56 Expressions

The expression C .this is legal in the statement part of an enclosing class or object definition with simple name C. It stands for the object being defined by the innermost such definition. If the expression’s expected type is a singleton type, or C .this occurs as the prefix of a selection, its type is C .this.type, otherwise it is the self type of class C. A reference super.m in a template refers to the definition of m in the actual superclass (§5.1.2) of the template. A reference C .super.m refers to the definition of m in the actual superclass of the innermost enclosing class or object definition named C which encloses the reference. The definition m referred to via super or C .super must be concrete, or the template containing the reference must have an incomplete (§5.1.6) member m0 which overrides m. The super prefix may be followed by a mixin qualifier [M ], as in C .super[M ].x. This is called a mixin super reference. In this case, the reference is to the member of x in the (first) mixin class of C whose simple name is M. That member may not be abstract.

Example 6.3.1 Consider the following class deﬁnitions

class Root { val x = "Root" } class A extends Root { override val x = "A" ; val superA = super.x } class B extends Root { override val x = "B" ; val superB = super.x } class C extends A with B{ override val x = "C" ; val superC = super.x } class D extends A{ val superD = super.x } class E extends C with D{ val superE = super.x }

Then we have:

(new A).superA == "Root", (new B).superB == "Root" (new C).superA == "Root", (new C).superB == "A", (new C).superC == "A" (new D).superA == "Root", (new D).superD == "A" (new E).superA == "Root", (new E).superB == "A", (new E).superC == "A", (new E).superD == "C", (new E).superE == "C"

Note that the superB function returns different results depending on whether B is used as deﬁning class or as a mixin class.

Example 6.3.2 Consider the following class deﬁnitions:

class Shape { override def equals(other: Any) = ...; ... } trait Bordered extends Shape { val thickness: int; 6.4 Function Applications 57

override def equals(other: Any) = other match { case that: Bordered => super equals other && this.thickness == that.thickness case _ => false } ... } trait Colored extends Shape { val color: Color; override def equals(other: Any) = other match { case that: Colored => super equals other && this.color == that.color case _ => false } ... }

Both deﬁnitions of equals are combined in the class below.

trait BorderedColoredShape extends Shape with Bordered with Colored { override def equals(other: Any) = super[Bordered].equals(that) && super[Colored].equals(that) }

6.4 Function Applications

Syntax:

SimpleExpr ::= SimpleExpr ArgumentExprs

An application f (e1,..., en) applies the function f to the argument expressions e1,..., en. If f has a method type (T1,..., Tn)U, the type of each argument expression ei must conform to the corresponding parameter type Ti . If f has some value type, the application is taken to be equivalent to f .apply(e1,..., en), i.e. the application of an apply method deﬁned by f .

Evaluation of f (e1,..., en) usually entails evaluation of f and e1,..., en in that order. Each argument expression is converted to the type of its corresponding formal parameter. After that, the application is rewritten to the function’s right hand side, with actual arguments substituted for formal parameters. The result of evaluating the rewritten right-hand side is ﬁnally converted to the function’s declared result type, if one is given. The case of a formal parameter with a parameterless method type => T is treated specially. In this case, the corresponding actual argument expression is not evaluated before the application. Instead, every use of the formal parameter on the 58 Expressions right-hand side of the rewrite rule entails a re-evaluation of the actual argument expression. In other words, the evaluation order for def-parameters is call-by-name whereas the evaluation order for normal parameters is call-by-value.

6.5 Type Applications

Syntax:

SimpleExpr ::= SimpleExpr ‘[’ Types ‘]’

A type application e[T1,..., Tn] instantiates a polymorphic value e of type [a1 >: L1 <: U1,..., an >: Ln <: Un]S with argument types T1,..., Tn. Every argument type Ti must obey corresponding bounds Li and Ui . That is, for each i 1, ..., n, we must have L σ : T : U σ, where σ is the substitution [a : = i < i < i 1 = T ,..., a : T ]. The type of the application is Sσ. 1 n = n The function part e may also have some value type. In this case the type application is taken to be equivalent to e.apply[T1,..., Tn], i.e. the application of an apply method deﬁned by e. Type applications can be omitted if local type inference (§10) can infer best type parameters for a polymorphic functions from the types of the actual function arguments and the expected result type.

6.6 References to Overloaded Bindings

If a name f referenced in an identifier or selection is overloaded (§4.6), the context of the reference has to identify a unique alternative of the overloaded binding. The way this is done depends on whether or not f is used as a function. Let A be the set of all type alternatives of f . Assume first that f appears as a function in an application, as in f (args). If there is precisely one alternative in A which is a (possibly polymorphic) method type whose arity matches the number of arguments given, that alternative is chosen. Otherwise, let Ts be the vector of types obtained by typing each argument with a missing expected type. One determines first the set of applicable alternatives. A method type alternative is applicable if each type in Ts is compatible with the corresponding formal parameter type in the alternative, and, if the expected type is defined, the method’s result type is compatible to it. A polymorphic method type is applicable if local type inference can determine type arguments so that the instantiated method type is applicable. Here, a type T is compatible to a type U if T conforms to U after applying implicit conversions (§3.7). 6.6 References to Overloaded Bindings 59

Let B be the set of applicable alternatives. It is an error if B is empty. Otherwise, one chooses the most specific alternative among the alternatives in B, according to the following definition of being “more specific”.

• A method type (Ts)U is more speciﬁc than some other type S if S is applicable to arguments (ps ) of types Ts.

• A polymorphic method type [a1 >: L1 <: U1,..., an >: Ln <: Un]T is more speciﬁc than some other type S if T is more speciﬁc than S under the assumption that for i 1, ..., n each a is an abstract type name bounded = i from below by Li and from above by Ui .

• Any other type is always more speciﬁc than a parameterized method type or a polymorphic type.

It is an error if there is no unique alternative in B which is more specific than all other alternatives in B. Assume next that f appears as a function in a type application, as in f [targs]. Then we choose an alternative in A which takes the same number of type parameters as there are type arguments in targs. It is an error if no such alternative exists, or if it is not unique. Assume finally that f does not appear as a function in either an application or a type application. If an expected type is given, let B be the set of those alternatives in A which are compatible to it. Otherwise, let B be the same as A . We choose in this case the most specific alternative among all alternatives in B. It is an error if there is no unique alternative in B which is more specific than all other alternatives in B.

Example 6.6.1 Consider the following deﬁnitions:

class A extends B {} def f(x: B, y: B) = ... def f(x: A, y: B) = ... val a: A; val b: B

Then the application f(b, b) refers to the first definition of f whereas the application f(a, a) refers to the second. Assume now we add a third overloaded definition

def f(x: B, y: A) = ...

Then the application f(a, a) is rejected for being ambiguous, since no most spe- ciﬁc applicable signature exists. 60 Expressions

6.7 Instance Creation Expressions

Syntax:

SimpleExpr ::= new Template

A simple instance creation expression is of the form new c where c is a constructor invocation (§5.1.1). Let T be the type of c. Then T must denote a (a type instance of) a non-abstract subclass of scala.AnyRef which conforms to its self type (§5.2). The expression is evaluated by creating a fresh object of type T which is is initialized by evaluating c. The type of the expression is T ’s self type (which might be less speciﬁc than T ). A general instance creation expression is of the form

new sc with mc1 with ... with mcn {stats} where n 0, sc as well as mc ,..., mc are constructor invocations (of types ≥ 1 n S,T1,..., Tn, say) and stats is a statement sequence containing initializer statements and member definitions (§5.1.4). The type of such an instance creation expression is then the compound type S with T1 with ... with Tn {R }, where {R } is a refinement (§3.2.5) which declares exactly those members of stats that override a member of S or T1,..., Tn. For this type to be well-formed, R may not reference types defined in stats which do not themselves form part of R. The instance creation expression is evaluated by creating a fresh object, which is initialized by evaluating the expression template.

Example 6.7.1 Consider the class

abstract class C{ type T; val x: T; def f(x: T): AnyRef } and the instance creation expression

C{ type T = Int; val x: T = 1; def f(x: T): T = y; val y: T = 2 }

Then the created object’s type is:

C{ type T = Int; val x: T; def f(x: T): T }

The value y is missing from the type, since y does not override a member of C.

6.8 Blocks

Syntax: 6.9 Prefix, Infix, and Postfix Operations 61

BlockExpr ::= ‘{’ Block ‘}’ Block ::= [{BlockStat ‘;’} ResultExpr]

A block expression {s1; ...; sn; e } is constructed from a sequence of block statements s1,..., sn and a final expression e. The final expression can be omitted, in which case the unit value () is assumed. The expected type of the final expression e is the expected type of the block. The expected type of all preceding statements is missing.

The type of a block s1; ...; sn; e is usually the type of e. That type must be equivalent to a type which does not refer to an entity defined locally in the block. If this condition is violated, but a fully defined expected type is given, the type of the block is instead assumed to be the expected type. Evaluation of the block entails evaluation of its statement sequence, followed by an evaluation of the final expression e, which defines the result of the block.

Example 6.8.1 Written in isolation, the block

{ class C extends B{...}; new C} is illegal, since its type refers to class C, which is deﬁned locally in the block. However, when used in a deﬁnition such as

val x: B = { class C extends B{...}; new C} the block is well-formed, since the problematic type C can be replaced by the expected type B.

6.9 Prefix, Infix, and Postfix Operations

Syntax:

PostfixExpr ::= InfixExpr [id] InfixExpr ::= PrefixExpr | InfixExpr id PrefixExpr PrefixExpr ::= [‘-’ | ‘+’ | ‘!’ | ‘~’] SimpleExpr

Expressions can be constructed from operands and operators. A prefix operation op e consists of a prefix operator op, which must be one of the identifiers ‘+’, ‘-’, ‘!’, or ‘~’, and a simple expression e. The expression is equivalent to the postfix method application e.op. Prefix operators are different from normal function applications in that their operand expression need not be atomic. For instance, the input sequence -sin(x) is read as -(sin(x)), whereas the function application negate sin(x) would be 62 Expressions parsed as the application of the infix operator sin to the operands negate and (x). An infix or postfix operator can be an arbitrary identifier. Infix operators have precedence and associativity defined as follows: The precedence of an infix operator is determined by the operator’s first character. Characters are listed below in increasing order of precedence, with characters on the same line having the same precedence.

(all letters) | ^ & < > = ! : + - * /% (all other special characters)

That is, operators starting with a letter have lowest precedence, followed by operators starting with ‘|’, etc. The associativity of an operator is determined by the operator’s last character. Op- erators ending with a colon ‘:’ are right-associative. All other operators are left- associative. Precedence and associativity of operators determine the grouping of parts of an expression as follows.

• If there are several inﬁx operations in an expression, then operators with higher precedence bind more closely than operators with lower precedence.

• If there are consecutive inﬁx operations e0 op1 e1 op2 ...opn en with operators op1,..., opn of the same precedence, then all these operators must have the same associativity. If all operators are left-associative, the sequence is inter-

preted as (...(e0 op1 e1) op2 ...) opn en. Otherwise, if all operators are right- associative, the sequence is interpreted as e0 op1 (e1 op2 (...opn en)...). • Postﬁx operators always have lower precedence than inﬁx operators. E.g.

e1 op1 e2 op2 is always equivalent to (e1 op1 e2) op2.

A postﬁx operation e op is interpreted as e.op. A left-associative binary operation e1 op e2 is interpreted as e1.op(e2). If op is right-associative, the same operation is interpreted as (val x=e1; e2.op(x )), where x is a fresh name.

6.10 Typed Expressions

Syntax: 6.11 Method closures 63

Expr1 ::= PostfixExpr [‘:’ Type1]

The typed expression e : T has type T . The type of expression e is expected to conform to T . The result of the expression is the value of e converted to type T .

Example 6.10.1 Here are examples of well-typed and illegally typed expressions.

1: int // legal, of type int 1: long // legal, of type long // 1: string // illegal

6.11 Method closures

Syntax:

MethodClosure ::= ‘.’ Id {‘.’ Id | TypeArgs | ArgumentExprs}

A method closure .i d starts with a period and an identiﬁer, which may be followed by selections and type- and value-arguments. This expression is equivalenet to an anonymous function x => x.i d where x is a fresh parameter name. No type for x is given; hence this type needs to be inferrable from the context of the expression.

Example 6.11.1 The following method returns the n’th column of a given list of row-lists xss, using methods map, drop and head deﬁned in class scala.List.

def column[T](xss: List[List[T]], n: int): List[T] = xss.map(.drop(i)).map(.head)

6.12 Assignments

Syntax:

Expr1 ::= Designator ‘=’ Expr | SimpleExpr ArgumentExprs ‘=’ Expr

The interpretation of an assignment to a simple variable x = e depends on the deﬁnition of x. If x denotes a mutable variable, then the assignment changes the current value of x to be the result of evaluating the expression e. The type of e is expected to conform to the type of x. If x is a parameterless function deﬁned in some template, and the same template contains a setter function x_= as member, then the assignment x = e is interpreted as the invocation x_=(e ) of that setter function. Analogously, an assignment f .x = e to a parameterless function x is interpreted as the invocation f .x_=(e ). 64 Expressions

An assignment f (args) = e with a function application to the left of the “=’ operator is interpreted as f .update(args, e ), i.e. the invocation of an update function deﬁned by f .

Example 6.12.1 Here is the usual imperative code for matrix multiplication.

def matmul(xss: Array[Array[double]], yss: Array[Array[double]]) = { val zss: Array[Array[double]] = new Array(xss.length, yss.length); var i = 0; while (i < xss.length) { var j = 0; while (j < yss(0).length) { var acc = 0.0; var k = 0; while (k < yss.length) { acc = acc + xs(i)(k) * yss(k)(j); k = k + 1 } zss(i)(j) = acc; j = j + 1 } i = i + 1 } zss }

Desugaring the array accesses and assignments yields the following expanded version:

def matmul(xss: Array[Array[double]], yss: Array[Array[double]]) = { val zss: Array[Array[double]] = new Array(xss.length, yss.length); var i = 0; while (i < xss.length) { var j = 0; while (j < yss(0).length) { var acc = 0.0; var k = 0; while (k < yss.length) { acc = acc + xss.apply(i).apply(k) * yss.apply(k).apply(j); k = k + 1 } zss.apply(i).update(j, acc); j = j + 1 } i = i + 1 } zss 6.13 Conditional Expressions 65

}

6.13 Conditional Expressions

Syntax:

Expr1 ::= if ‘(’ Expr ‘)’ Expr [[‘;’] else Expr]

The conditional expression if (e1) e2 else e3 chooses one of the values of e2 and e3, depending on the value of e1. The condition e1 is expected to conform to type boolean. The then-part e2 and the else-part e3 are both expected to conform to the expected type of the conditional expression. The type of the conditional expression is the least upper bound of the types of e1 and e2. A semicolon preceding the else symbol of a conditional expression is ignored.

The conditional expression is evaluated by evaluating ﬁrst e1. If this evaluates to true, the result of evaluating e2 is returned, otherwise the result of evaluating e3 is returned. A short form of the conditional expression eliminates the else-part. The conditional expression if (e1) e2 is evaluated as if it was if (e1) e2 else (). The type of this expression is unit and the then-part e2 is also expected to conform to type unit.

6.14 While Loop Expressions

Syntax:

Expr1 ::= while ‘(’ Expr ’)’ Expr

The while loop expression while (e1) e2 is typed and evaluated as if it was an application of whileLoop (e1)(e2) where the hypothetical function whileLoop is deﬁned as follows.

def whileLoop(cond: => Boolean)(body: => Unit): Unit = if (cond) { body ; while(cond)(body) } else {}

Example 6.14.1 The loop

while (x!=0){y=y+1/x;x=x-1}

Is equivalent to the application

whileLoop (x != 0) { y = y + 1/x ; x = x - 1 } 66 Expressions

Note that this application will never produce a division-by-zero error at run-time, since the expression (y = 1/x) will be evaluated in the body of while only if the condition parameter is false.

6.15 Do Loop Expressions

Syntax:

Expr1 ::= do Expr [‘;’] while ‘(’ Expr ’)’

The do loop expression do e1 while (e2) is typed and evaluated as if it was the expression (e1 ; while (e2) e1). A semicolon preceding the while symbol of a do loop expression is ignored.

6.16 Comprehensions

Syntax:

Expr1 ::= for ‘(’ Enumerators ‘)’ [yield] Expr Enumerator ::= Generator {‘;’ Enumerator} Enumerator ::= Generator | Expr Generator ::= val Pattern1 ‘<-’ Expr

A comprehension for (enums) yield e evaluates expression e for each binding generated by the enumerators enums. Enumerators start with a generator, which can be followed by further generators or filters. A generator val p <- e produces bindings from an expression e which is matched in some way against pattern p.A filter is an expressions which restricts enumerated bindings. The precise meaning of generators and filters is defined by translation to invocations of four methods: map, filter, flatMap, and foreach. These methods can be implemented in different ways for different carrier types. The translation scheme is as follows. In a first step, every generator val p <- e, where p is not a pattern variable, is replaced by

val p <- e.filter { case p => true; case _ => false }

Then, the following rules are applied repeatedly until all comprehensions have been eliminated.

• A generator val p <- e followed by a ﬁlter f is translated to a single generator val p <- e.filter(x1,..., xn => f ) where x1,..., xn are the free variables of p. 6.16 Comprehensions 67

• A for-comprehension for (val p <- e ) yield e0 is translated to e.map { case p => e0 }.

• A for-comprehension for (val p <- e ) e0 is translated to e.foreach { case p => e0 }. • A for-comprehension

for (val p <- e; val p0 <- e0 ...) yield e00 ,

where ... is a (possibly empty) sequence of generators or ﬁlters, is translated to

e.flatmap { case p => for (val p0 <- e0 ...) yield e00 }.

• A for-comprehension

for (val p <- e; val p0 <- e0 ...) e00 .

where ... is a (possibly empty) sequence of generators or ﬁlters, is translated to

e.foreach { case p => for (val p0 <- e0 ...) e00 }.

Example 6.16.1 the following code produces all pairs of numbers between 1 and n 1 whose sums are prime. − for { val i <- range(1, n); val j <- range(1, i); isPrime(i+j) } yield Pair (i, j)

The for-comprehension is translated to:

range(1, n) .flatMap { case i => range(1, i) .filter { j => isPrime(i+j) } .map { case j => Pair(i, j) } }

Example 6.16.2 For comprehensions can be used to express vector and matrix al- gorithms concisely. For instance, here is a function to compute the transpose of a given matrix:

def transpose[a](xss: Array[Array[a]]) { for (val i <- Array.range(0, xss(0).length)) yield Array(for (val xs <- xss) yield xs(i)) 68 Expressions

Here is a function to compute the scalar product of two vectors:

def scalprod(xs: Array[double], ys: Array[double]) { var acc = 0.0; for (val Pair(x, y) <- xs zip ys) acc = acc + x * y; acc }

Finally, here is a function to compute the product of two matrices. Compare with the imperative version of Example 6.12.1.

def matmul(xss: Array[Array[double]], yss: Array[Array[double]]) = { val ysst = transpose(yss); for (val xs <- xs) yield for (val yst <- ysst) yield scalprod(xs, yst) }

The code above makes use of the fact that map, flatmap, filter, and foreach are deﬁned for members of class scala.Array.

6.17 Return Expressions

Syntax:

Expr1 ::= return [Expr]

A return expression return e must occur inside the body of some enclosing named method or function f . This function must have an explicitly declared result type, and the type of e must conform to it. The return expression evaluates the expression e and returns its value as the result of f . The evaluation of any statements or expressions following the return expression is omitted. The type of a return expression is scala.All.

6.18 Throw Expressions

Syntax:

Expr1 ::= throw Expr

A throw expression throw e evaluates the expression e. The type of this expression must conform to Throwable. If e evaluates to an exception reference, evaluation is aborted with the thrown exception. If e evaluates to null, evaluation is instead aborted with a NullPointerException. If there is an active try expression (§6.19) 6.19 Try Expressions 69 which handles the thrown exception, evaluation resumes with the handler; otherwise the thread executing the throw is aborted. The type of a throw expression is scala.All.

6.19 Try Expressions

Syntax:

Expr1 ::= try ‘{’ Block ‘}’ [catch Expr] [finally Expr]

A try expression try { b } catch e evaluates the block b. If evaluation of b does not cause an exception to be thrown, the result of b is returned. Otherwise the handler e is applied to the thrown exception. Let pt be the expected type of the try expression. The block b is expected to conform to pt. The handler e is expected conform to type scala.PartialFunction[scala.Throwable, pt]. The type of the try expression is the least upper bound of the type of b and the result type of e. A try expression try { b } finally e evaluates the block b. If evaluation of b does not cause an exception to be thrown, the expression e is evaluated. If an exception is thrown during evaluation of e, the evaluation of the try expression is aborted with the thrown exception. If no exception is thrown during evaluation of e, the result of b is returned as the result of the try expression. If an exception is thrown during evaluation of b, the ﬁnally block e is also evaluated. If another exception e is thrown during evaluation of e, evaluation of the try expression is aborted with the thrown exception. If no exception is thrown during evaluation of e, the original exception thrown in b is re-thrown once evaluation of e has completed. The block b is expected to conform to the expected type of the try expression. The ﬁnally expression e is expected to conform to type unit.

A try expression try { b } catch e1 finally e2 is a shorthand for try { try { b } catch e1 } finally e2.

6.20 Anonymous Functions

Syntax:

Expr1 ::= Bindings ‘=>’ Expr ResultExpr ::= Bindings ‘=>’ Block Bindings ::= ‘(’ Binding {‘,’ Binding ‘)’ | id [‘:’ Type1] Binding ::= id [‘:’ Type]

The anonymous function (x1: T1,..., xn: Tn) => e maps parameters xi of types Ti to a result given by expression e. The scope of each formal parameter xi is e. 70 Expressions

Formal parameters must have pairwise distinct names. If the expected type of the anonymous function is of the form scala.Functionn[S1,..., Sn, R ], the expected type of e is R and the type Ti of any of the parameters xi can be omitted, in which case Ti = Si is assumed. If the expected type of the anonymous function is some other type, all formal parameter types must be explicitly given, and the expected type of e is missing. The type of the anonymous function is scala.Functionn[S1,..., Sn, T ], where T is the type of e. T must be equivalent to a type which does not refer to any of the formal parameters xi . The anonymous function is evaluated as the instance creation expression

scala.Functionn[T1,..., Tn, T ]{ def apply(x1: T1,..., xn: Tn): T = e }

In the case of a single formal parameter, (x: T ) => e and (x ) => e can be ab- breviated to x: T => e, and x => e, respectively.

Example 6.20.1 Examples of anonymous functions:

x => x // The identity function

f => g => x => f(g(x)) // Curried function composition

(x: Int,y: Int) => x + y // A summation function

() => { count = count + 1; count } // The function which takes an // empty parameter list (), // increments a non-local variable // ‘count’ and returns the new value.

6.21 Statements

Syntax:

BlockStat ::= Import | Def | {LocalModifier} TmplDef | Expr | TemplateStat ::= Import | {AttributeClause} {Modifier} Def | {AttributeClause} {Modifier} Dcl | Expr 6.21 Statements 71

Statements occur as parts of blocks and templates. A statement can be an import, a definition or an expression, or it can be empty. Statements used in the template of a class definition can also be declarations. An expression that is used as a statement can have an arbitrary value type. An expression statement e is evaluated by evaluating e and discarding the result of the evaluation. Block statements may be definitions which bind local names in the block. The only modifiers allowed in block-local definitions are modifiers abstract, final, or sealed preceding a class or object definition. With the exception of overloaded definitions (§4.6), a statement sequence making up a block or template may not contain two definitions or declarations that bind the same name in the same namespace. Evaluation of a statement sequence entails evaluation of the statements in the order they are written.

Chapter 7 Pattern Matching

7.1 Patterns

Syntax:

Pattern ::= SimplePattern {Id SimplePattern} | varid ‘:’ Type | ‘_’ ‘:’ Type SimplePattern ::= varid | ‘_’ | literal | StableId {‘(’ [Patterns] ‘)’} | XmlPattern Patterns ::= Pattern {‘,’ Pattern}

For clarity, this section deals with a subset of the Scala pattern language. The extended Scala pattern language, which is described below, adds more flexible variable binding and regular hedge expressions. A pattern is built from constants, constructors, variables and regular operators. Pat- tern matching tests whether a given value (or sequence of values) has the shape defined by a pattern, and, if it does, binds the variables in the pattern to the corresponding components of the value (or sequence of values). The same variable name may not be bound more than once in a pattern. Pattern matching is always done in a context which supplies an expected type of the pattern. We distinguish the following kinds of patterns. A variable pattern x is a simple identifier which starts with a lower case letter. It matches any value, and binds the variable name to that value. The type of x is the expected type of the pattern as given from outside. A special case is the wild-card pattern _ which is treated as if it was a fresh variable. 74 Pattern Matching

A typed pattern x : T consists of a pattern variable x and a simple type T . The type T may be a class type or a compound type; it may not contain a refinement (§3.2.5). This pattern matches any value of type T and binds the variable name to that value. T must conform to the pattern’s expected type. The type of x is T . A pattern literal l matches any value that is equal (in terms of ) to it. It’s type == must conform to the expected type of the pattern. A named pattern constant r is a stable identifier (§3.1). To resolve the syntactic over- lap with a variable pattern, a named pattern constant may not be a simple name starting with a lower-case letter. The type of r must conform to the expected type of the pattern. The pattern matches any value v such that $r$ == $v$ (§12.1). A constructor pattern c(p )...(p ) where n 0 consists of an identifier c, followed 1 n ≥ by component patterns p1,..., pn. The constructor c is either a simple name or a qualified name r.i d where r is a stable identifier. It refers to a (possibly overloaded) function which has one alternative of result type class C, and which may not have other overloaded alternatives with a class constructor type as result type. Further- more, the respective type parameters and value parameters of (said alternative of) c and of the primary constructor function of class C must be the same, after renaming corresponding type parameter names. If C is monomorphic, then C must conform to the expected type of the pattern, and the formal parameter types of C’s primary constructor are taken as the expected types of the component patterns p1,..., pn. If C is polymorphic, then there must be a unique type application instance of it such that the instantiation of C conforms to the expected type of the pattern. The instantiated formal parameter types of C’s primary constructor are then taken as the expected types of the component patterns p1,..., pn. The pattern matches all objects created from constructor invocations c(v1)...(vn) where each component pattern pi matches the corresponding value vi . An infix operation pattern p id p’ is a shorthand for the constructor pattern id_class(p)(p’). The precedence and associativity of operators in patterns is the same as in expressions (§6.9).

Example 7.1.1 Some examples of patterns are:

1. The pattern ex: IOException matches all instances of class IOException, binding variable ex to the instance. 2. The pattern (x, _) matches pairs of values, binding x to the ﬁrst component of the pair. The second component is matched with a wildcard pattern. 3. The pattern x :: y :: xs matches lists of length 2, binding x to the lists’s ≥ ﬁrst element, y to the list’s second element, and xs to the remainder.

7.1.1 Regular Pattern Matching

Syntax: 7.1 Patterns 75

Pattern ::= Pattern1 { ‘|’ Pattern1 } Pattern1 ::= varid ‘:’ Type | ‘_’ ‘:’ Type | Pattern2 Pattern2 ::= [varid ‘@’] Pattern3 Pattern3 ::= SimplePattern [ ’*’ | ’?’ | ’+’ ] | SimplePattern { id’ SimplePattern } SimplePattern ::= ‘_’ | varid | Literal | StableId [ ‘(’ [Patterns] ‘)’ ] | ‘(’ [Patterns] ‘)’ Patterns ::= Pattern {‘,’ Pattern} id’ ::= id but not ’*’ | ’?’ | ’+’ | ‘@’ | ‘|’

We distinguish between tree patterns and hedge patterns (hedges are ordered sequences of trees). A tree pattern describes a set of matching trees (like above). A hedge pattern describes a set of matching hedges. Both kinds of patterns may contain variable bindings which serve to extract constituents of a tree or hedge. The type of a patterns and the expected types of variables within patterns are determined by the context and the structure of the patterns. The last case ensures that a variable bound to a hedge pattern will have a sequence type. The following patterns are added: A hedge pattern p ,..., p where n 0 is a sequence of patterns separated by com- 1 n ≥ mas and matching the hedge described by the components. Hedge patterns may appear as arguments to constructor applications, or nested within a another hedge pattern if grouped with parentheses. Note that empty hedge patterns are allowed. The type of tree patterns that appear in a hedge pattern is the expected type as determined from the enclosing constructor. A fixed-length argument pattern is a special hedge pattern where where all pi are tree patterns. A choice pattern p ... p is a choice among several alternatives, which may not 1| | n contain variable-binding patterns. It matches every tree and every hedge matched by at least one of its alternatives. Note that the empty sequence may appear as an alternative. An option pattern p? is an abbreviation for (p ). A choice is a tree pattern | if all its branches are tree patterns. In this case, all branches must conform to the expected type and the type of the choice is the least upper bound of the branches. Otherwise, its type is determined by the enclosing hedge pattern it is part of. An iterated pattern p matches zero, one or more occurrences of items matched by ∗ p, where p may be either a tree pattern or a hedge pattern. p may not contain a variable-binding. A non-empty iterated pattern p is an abbreviation for (p,p ). + ∗ The treatment of the following patterns changes with to the previous section: A constructor pattern c(p) consists of a simple type c followed by a pattern p. If c 76 Pattern Matching designates a monomorphic case class, then it must conform to the expected type of the pattern, the pattern must be a fixed length argument pattern p1,..., pn whose length corresponds to the number of arguments of c’s primary constructor. The expected types of the component patterns are then taken from the formal parameter types of (said) constructor. If c designates a polymorphic case class, then there must be a unique type application instance of it such that the instantiation of c conforms to the expected type of the pattern. The instantiated formal parameter types of c’s primary constructor are then taken as the expected types of the component patterns p1,..., pn. In both cases, the pattern matches all objects created from constructor invocations c(v1,..., vn) where each component pattern pi matches the corresponding value vi . If c does not designate a case class, it must be a subclass of Seq[T ]. In that case p may be an arbitrary sequence pattern. Value patterns in p are expected to conform to type T , and the pattern matches all objects whose elements() method returns a sequence that matches p. The pattern (p) is regarded as equivalent to the pattern p, if p is a nonempty sequence pattern. The empty tuple () is a shorthand for the constructor pattern Unit. A variable-binding x@p is a simple identifier x which starts with a lower case letter, together with a pattern p. It matches every item (tree or hedge) matched by p, and in addition binds it to the variable name. If p is a tree pattern of type T , the type of x is also T . If p is a hedge pattern enclosed by constructor c :Seq[T ], then the type < of x is List[T ] where T is the expected type as dictated by the constructor. Regular expressions that contain variable bindings may be ambiguous, i.e. there might be several ways to match a sequence against the pattern. In these cases, the right-longest policy applies: patterns that appear more to the right than others in a sequence take precedence in case of overlaps.

Example 7.1.2 Some examples of patterns are:

1. The pattern ex: IOException matches all instances of class IOException, binding variable ex to the instance. 2. The pattern Pair(x, _) matches pairs of values, binding x to the ﬁrst component of the pair. The second component is matched with a wildcard pattern.

3. The pattern List( x, y, xs @ _ * ) matches lists of length 2, binding x to ≥ the list’s ﬁrst element, y to the list’s second element, and xs to the remainder, which may be empty. 4. The pattern List( 1, x@(( ’a’ | ’b’ )+),y,_ ) matches a list that contains 1 as its ﬁrst element, continues with a non-empty sequence of ’a’s and ’b’s, followed by two more elements. The sequence ’a’s and ’b’s is bound to x, and the next to last element is bound to y.

5. The pattern List( x@( ’a’* ), ’a’+ ) matches a non-empty list of ’a’s. Because of the shortest match policy, x will always be bound to the empty sequence. 7.2 Pattern Matching Expressions 77

6. The pattern List( x@( ’a’+ ), ’a’* ) also matches a non-empty list of ’a’s. Here, x will always be bound to the sequence containing one ’a’

7.2 Pattern Matching Expressions

Syntax:

BlockExpr ::= ‘{’ CaseClause {CaseClause} ‘}’ CaseClause ::= case Pattern [‘if’ PostfixExpr] ‘=>’ Block

A pattern matching expression case p1 => b1 ... case pn => bn consists of a number n 1 of cases. Each case consists of a (possibly guarded) pattern p and ≥ i a block bi . The scope of the pattern variables in pi is the corresponding block bi . The expected type of a pattern matching expression must in part be defined. It must be either scala.Function1[Tp, Tr ] or scala.PartialFunction[Tp, Tr ], where the argument type Tp must be fully determined, but the result type Tr may be undetermined. All patterns are typed relative to the expected type Tp (§7.1). The expected type of every block bi is Tr . Let Tb be the least upper bound of the types of all blocks bi . The type of the pattern matching expression is then the required type with Tr replaced by Tb (i.e. the type is either scala.Function[Tp, Tb] or scala.PartialFunction[Tp, Tb]. When applying a pattern matching expression to a selector value, patterns are tried in sequence until one is found which matches the selector value (§7.1). Say this case is case p b . The result of the whole expression is then the result of evaluating b , i ⇒ i i where all pattern variables of pi are bound to the corresponding parts of the selector value. If no matching pattern is found, a scala.MatchError exception is thrown. The pattern in a case may also be followed by a guard suffix if e with a boolean expression e. The guard expression is evaluated if the preceding pattern in the case matches. If the guard expression evaluates to true, the pattern match succeeds as normal. If the guard expression evaluates to false, the pattern in the case is considered not to match and the search for a matching pattern continues. In the interest of efficiency the evaluation of a pattern matching expression may try patterns in some other order than textual sequence. This might affect evaluation through side effects in guards. However, it is guaranteed that a guard expression is evaluated only if the pattern it guards matches.

Example 7.2.1 Often, pattern matching expressions are used as arguments of the match method, which is predeﬁned in class Any (§12.1) and is implemented there by postﬁx function application. Here is an example:

def length [a] (xs: List[a]) = xs match { case Nil => 0 case x :: xs1 => 1 + length (xs1) 78 Pattern Matching

}

In an application of match such as the one above, the expected type of all patterns is the type of the qualiﬁer of match. In the example above, the expected type of the patterns Nil and x :: xs1 would be List[a], the type of xs. Chapter 8 Views

Views are user-deﬁned, implicit coercions that are automatically inserted by the compiler.

8.1 View Deﬁnition

A view definition is a normal function definition with one value parameter where the name of the defined function is view.

Example 8.1.1 The following deﬁnes an implicit coercion function from strings to lists of characters.

def view(xs: String): List[char] = if (xs.length() == 0) List() else xs.charAt(0) :: xs.substring(1);

8.2 View Application

View applications are inserted implicitly in two situations.

1. Around an expression e of type T , if T does not conform to the expression’s expected type PT . 2. In a selection e.m with e of type T , if the selector m does not denote a member of T .

In the ﬁrst case, a view method view is searched which is applicable to e and whose result type conforms to PT . If such a method is found, the expression e is converted to view(e). 80 Views

In the second case, a view method view is searched which is applicable to e and whose result contains a member named m. If such a method is found, the selection e.m is converted to view(e).m

8.3 Finding Views

Searching a view which is applicable to an expression e of type T is a three-step process.

1. First, the set A of available views is determined. A is the smallest set such that:

(a) If a unary method called view is accessible without qualifier anywhere on the path of the program tree that leads from e to the root of the tree (describing the whole compilation unit), then that method is in the set A . Methods are accessible without qualifier because they are locally defined in an enclosing scope, or imported into an enclosing scope, or inherited by an enclosing class. (b) If a unary method called view is a member of an object C such that there is a base class C of T with the same name as the object and defined in the same scope, then that method is in the set A .

2. Then, among all the methods in A the set of all applicable views B is determined. A view method is applicable if it can be applied to values of type T , and another condition is satisﬁed which depends on the context of the view application:

(a) If the view is a conversion to a given prototype PT , then the view’s result type must conform to PT . (b) If the view is a conversion in a selection with member m, then the view’s result type must contain a member named m.

Note that in the determining of view applicability, we do not permit further views to be inserted. I.e. a view is applicable to an expression e of type T if it can be applied to e, without a further view conversion of e to the view’s formal parameter type. Likewise, a view’s result type must conform to a given prototype directly, no second view conversion is allowed.

3. It is an error if the set of applicable views B is empty. For non-empty B, the view method which is most speciﬁc (§6.6) in B is selected. It is an error if no most speciﬁc view exists, or if it is not unique.

Example 8.3.1 Consider the following situation. 8.4 View-Bounds 81

class A; class B extends A; class C; object B{ def view(x: B): C = ... } object Test with Application { def view(x: A): C = ... val x: C = new B; }

For the expression new B there are two available views. The view defined in object B is available since its associated class is (a superclass of) the expression’s type B. The view defined in object Test is available since it is accessible without qualification at the point of the expression new B. Both views are also applicable since they map values of type B to results of type C. However, the view defined in object B is more specific than the view defined in object Test. Hence, the last statement in the example above is implicitly augmented to

val x: C = B.view(new B)

8.4 View-Bounds

Syntax:

TypeParam ::= id [>: Type] [<% Type]

A type parameter a may have a view bound a <% T instead of a regular upper bound a <: T. In that case the type parameter may be instantiated to any type S which is convertible by application of a view method to the view bound T. Here, we assume there exists an always available identity view method

def view[a](x: a): a = x .

Hence, the type parameter a can always be instantiated to subtypes of the view bound T, just as if T was a regular upper bound. View bounds for type parameters behave analogously to upper bounds wrt to type conformance (§3.5.2), variance checking (§4.4), and overriding (§5.1.5). Methods or classes with view-bounded type parameters implicitly take view functions as parameters. For every view-bounded type parameter a <% T one adds an implicit value parameter view: a => T. When instantiating the type parameter a to some type S, the most speciﬁc applicable view method from type S to type T is selected, according to the rules of §8.3. This method is then passed as actual argument to the corresponding view parameter. 82 Views

Implicit view parameters of a method or class are then taken as available view methods in its body.

Example 8.4.1 Consider the following deﬁnition of a trait Comparable and a view from strings to that trait.

trait Comparable[a] { def less(x: a): boolean }

object StringsAreComparable { def view(x: String): Comparable[String] = new Comparable[String] { def less(y: String) = x.compareTo(y) < 0 } }

Now, deﬁne a binary tree with a method insert which inserts an element in the tree and a method elements which returns a sorted list of all elements of the tree. The tree is deﬁned for all types of elements a that are viewable as Comparable[a].

trait Tree[a <% Comparable[a]] { def insert(x: a): Tree[a] = this match { case Empty() => new Node(x, Empty(), Empty()) case Node(elem, l, r) => if (x == elem) this else if (x less elem) Node(elem, l insert x, r) else Node(elem, l, r insert x); } def elements: List[a] = this match { case Empty() => List() case Node(elem, l, r) => l.elements ::: List(elem) ::: r.elements } } case class Empty[a <% Comparable[a]]() extends Tree[a]; case class Node[a <% Comparable[a]](elem: a, l: Tree[a], r: Tree[a]) extends Tree[a];

Finally, deﬁne a test program which builds a tree from all command line argument strings and then prints out the elements as a sorted sequence.

object Test { import StringsAreComparable.view;

def main(args: Array[String]) = { var t: Tree[String] = Empty(); 8.4 View-Bounds 83

for (val s <- args) { t = t insert s } System.out.println(t.elements) } }

Note that the deﬁnition var t: Tree[String] = Empty(); is legal because at that point a view method from String to Comparable[String] has been imported and is therefore accessible without a preﬁx. The imported view method is passed as an implicit argument to the Empty constructor. Here is the Test program again, this time with implicit views made visible:

object Test { import StringsAreComparable.view;

def main(args: Array[String]) = { var t: Tree[String] = Empty(StringsAreComparable.view); for (val s <- args) { t = t insert s } System.out.println(t.elements) } }

And here are the tree classes with implicit views added:

trait Tree[a <% Comparable[a]](view: a => Comparable[a]) { def insert(x: a): Tree[a] = this match { case Empty(_) => new Node(x, Empty(view), Empty(view)) case Node(_, elem, l, r) => if (x == elem) this else if (view(x) less elem) Node(view, elem, l insert x, r) else Node(view, elem, l, r insert x); } def elements: List[a] = this match { case Empty(_) => List() case Node(_, elem, l, r) => l.elements ::: List(elem) ::: r.elements } } case class Empty[a <% Comparable[a]](view: a => Comparable[a]) extends Tree[a]; case class Node[a <% Comparable[a]](view: a => Comparable[a], elem: a, l: Tree[a], r: Tree[a]) extends Tree[a];

Note that views entail a certain run-time overhead because they need to be passed as additional arguments to view-bounded methods and classes. Furthermore, every application of a view entails the construction of an object which is often immedi- 84 Views ately discarded afterwards – see for instance with the translation of (x less elem) in the implementation of method insert above. It is expected that the latter cost can be absorbed largely or completely by compiler optimizations (which are, however, not yet implemented at the present stage).

8.5 Conditional Views

View methods might themselves have view-bounded type parameters; this allows the deﬁnition of conditional views.

Example 8.5.1 The following view makes lists comparable, provided the list element type is also comparable.

def view[a <% Comparable[a]](xs: List[a]): Comparable[List[a]] = new Comparable[List[a]] { def less (ys: List[a]): boolean = !ys.isEmpty && (xs.isEmpty || (xs.head less ys.head) || (xs.head == ys.head) && (xs.tail less ys.tail)) }

Note that the condition (xs.head less ys.head) invokes the less method of the list element type, which is unknown at the point of the deﬁnition of the view method. As usual, view-bounded type parameters are translated to implicit view arguments. In this case, the view method over lists would receive the view method over list elements as implicit parameter. Chapter 9 Top-Level Deﬁnitions

Syntax:

CompilationUnit ::= [package QualId ‘;’] {TopStat ‘;’} TopStat TopStat ::= {AttributeClause} {Modifier} TmplDef | Import | Packaging | QualId ::= id {‘.’ id}

A compilation unit consists of a sequence of packagings, import clauses, and class and object deﬁnitions, which may be preceded by a package clause. A compilation unit package p; stats starting with a package clause is equivalent to a compilation unit consisting of a single packaging package p { stats }. Implicitly imported into every compilation unit are, in that order : the package java.lang, the package scala, and the object scala.Predef (§12.4). Members of a later import in that order hide members of an earlier import.

9.1 Packagings

Syntax:

Packaging ::= package QualId ‘{’ {TopStat ‘;’} TopStat ‘}’

A package is a special object which defines a set of member classes, objects and packages. Unlike other objects, packages are not introduced by a definition. In- stead, the set of members of a package is determined by packagings. A packaging package p ds injects all definitions in ds as members into the package whose qualified name is p. If a definition in ds is labeled private, it is visible 86 Top-Level Definitions only for other members in the package. Selections p.m from p as well as imports from p work as for objects. However, unlike other objects, packages may not be used as values. It is illegal to have a package with the same fully qualified name as a module or a class. Top-level definitions outside a packaging are assumed to be injected into a special empty package. That package cannot be named and therefore cannot be imported. However, members of the empty package are visible to each other without qualification.

Example 9.1.1 The following example will create a hello world program as function main of module test.HelloWorld.

package test;

object HelloWord { def main(args: Array[String]) = System.out.println("hello world") } Chapter 10 Local Type Inference

To be completed.

Chapter 11 XML expressions and patterns

This chapter describes the syntactic structure of XML expressions and patterns. It follows as close as possible the XML 1.0 speciﬁcation [W3Cb], changes being man- dated by the possibility of embedding Scala code fragments.

11.1 XML expressions

XML expressions are expressions generated by the following production, where the opening bracket ‘<’ of the ﬁrst element must be in a position to start the lexical XML mode (see 1.5). Syntax:

XmlExpr ::= Element {Element}

Well-formedness constraints of the XML speciﬁcation apply, which means for instance that start tags and end tags must match, and attributes may only be deﬁned once, with the exception of constraints related to entity resolution. The following productions describe Scala’s extensible markup language, designed as close as possible to the W3C extensible markup language standard. Only the productions for attribute values and character data are changed. Scala does not support neither declarations, CDATA sections nor processing instructions. Entity references are not resolved at runtime. Syntax:

Element ::= EmptyElemTag | STag Content ETag

EmptyElemTag ::= ‘<’ Name {S Attribute} [S] ‘/>’ 90 XML expressions and patterns

STag ::= ‘<’ Name {S Attribute} [S] ‘>’ ETag ::= ‘’ Content ::= [CharData] {Content1 [CharData]} Content1 ::= Element | Reference | CDSect | PI | Comment | ScalaExpr

If an XML expression is a single element, its value is a runtime representation of an XML node (an instance of a subclass of scala.xml.Node). If the XML expression consists of more than one element, then its value is a runtime representation of a sequence of XML nodes (an instance of a subclass of scala.Seq[scala.xml.Node]). If an XML expression is an entity reference, CDATA section, processing instructions or a comments, it is represented by an instance of the corresponding Scala runtime class. By default, beginning and trailing whitespace in element content is removed, and consecutive occurrences of whitespace are replaced by a single space character \u0020. This behaviour can be changed to preserve all whitespace with a compiler option. Syntax:

Attribute ::= Name Eq AttValue

AttValue ::= ‘"’ {CharQ | CharRef} ‘"’ | ‘’’ {CharA | CharRef} ‘’’ | ScalaExp

ScalaExpr ::= ‘{’ expr ‘}’

CharData ::= { CharNoRef } without {CharNoRef}‘{’CharB {CharNoRef} and without {CharNoRef}‘]]>’{CharNoRef}

XML expressions may contain Scala expressions as attribute values or within nodes. In the latter case, these are embedded using a single opening brace ‘’ and ended by a closing brace ‘’. To express a single opening braces within XML text as generated by CharData, it must be doubled. Thus, ‘‘ represents the XML text ‘‘ and does not introduce an embedded Scala expression. Syntax:

BaseChar, Char, Comment, CombiningChar, Ideographic, NameChar, S, Reference ::= “as in W3C XML”

Char1 ::= Char without ‘<’ | ‘&’ CharQ ::= Char1 without ‘"’ 11.2 XML patterns 91

CharA ::= Char1 without ‘’’ CharB ::= Char1 without ’{’

Name ::= XNameStart {NameChar}

XNameStart ::= ‘_’ | BaseChar | Ideographic (as in W3C XML, but without ‘:’

11.2 XML patterns

XML patterns are patterns generated by the following production, where the opening bracket ‘<’ of the element patterns must be in a position to start the lexical XML mode (see 1.5). Syntax:

XmlPattern ::= ElementPattern {ElementPattern}

Well-formedness constraints of the XML speciﬁcation apply. If an XML pattern is a single element pattern, it expects the type of runtime representation of an XML tree, and matches exactly one instance of this type that has the same structure as described by the pattern. If an XML pattern consists of more than one element, then it expects the type of sequences of runtime representations of XML trees, and matches every sequence whose elements match the sequence described by the pattern. XML patterns may contain Scala patterns(7.2). Whitespace is treated the same way as in XML expressions. Patterns that are entity references, CDATA sections, processing instructions and comments match runtime representations which are the the same. By default, beginning and trailing whitespace in element content is removed, and consecutive occurrences of whitespace are replaced by a single space character \u0020. This behaviour can be changed to preserve all whitespace with a compiler option. Syntax:

ElemPattern ::= EmptyElemTagP | STagP ContentP ETagP

EmptyElemTagP ::= ’<’ Name [S] ’/>’ STagP ::= ’<’ Name [S] ’>’ ETagP ::= ’’ ContentP ::= [CharData] {(ElemPattern|ScalaPatterns) [CharData]} ContentP1 ::= ElemPattern 92 XML expressions and patterns

| Reference | CDSect | PI | Comment | ScalaPatterns ScalaPatterns ::= ’{’ patterns ’}’ Chapter 12 The Scala Standard Library

The Scala standard library consists of the package scala with a number of classes and modules. Some of these classes are described in the following.

12.1 Root Classes

The root of the Scala class hierarchy is formed by class Any. Every class in a Scala execution environment inherits directly or indirectly from this class. Class Any has two direct subclasses: AnyRef andAnyVal. The subclass AnyRef represents all values which are represented as objects in the underlying host system. Every user-defined Scala class inherits directly or indirectly from this class. Furthermore, every user-defined Scala class also inherits the trait scala.ScalaObject. Classes written in other languages still inherit from scala.AnyRef, but not from scala.ScalaObject. The class AnyVal has a fixed number subclasses, which describe values which are not implemented as objects in the underlying host system. Classes AnyRef and AnyVal are required to provide only the members declared in class Any, but implementations may add host-specific methods to these classes (for instance, an implementation may identify class AnyRef with its own root class for objects). The standard interfaces of these root classes is described by the following definitions.

package scala; abstract class Any {

/** Defined equality; abstract here */ def equals(that: Any): boolean; 94 The Scala Standard Library

/** Semantic equality between values of same type */ final def == (that: Any): boolean = this equals that

/** Semantic inequality between values of same type */ final def != (that: Any): boolean = !(this == that)

/** Hash code */ def hashCode(): Int = ...

/** Textual representation */ def toString(): String = ...

/** Type test */ def isInstanceOf[a]: Boolean = this match { case x: a => true case _ => false }

/** Type cast */ def asInstanceOf[a]: a = this match { case x: a => x case _ => if (this eq null) this else throw new ClassCastException() }

/** Pattern match */ def match[a, b](cases: a => b): b = cases(this); } final class AnyVal extends Any; class AnyRef extends Any { def equals(that: Any): boolean = this eq that; final def eq(that: Any): boolean = ...; // reference equality } trait ScalaObject extends AnyRef;

The type cast operation asInstanceOf has a special meaning (not expressed in the code above) when its type parameter is a numeric type. For any type T <: Double, and any numeric value v v.asInstanceIf[T] converts v to type T using the rules of Java’s numeric type cast operation. The conversion might truncate the numeric value (as when going from Long to Int or from Int to Byte) or it might lose precision (as when going from Double to Float or when converting between Long and Float). 12.2 Value Classes 95

12.2 Value Classes

Value classes are classes whose instances are not represented as objects by the underlying host system. All value classes inherit from class AnyVal. Scala implementations need to provide the value classes Unit, Boolean, Double, Float, Long, Int, Char, Short, and Byte (but are free to provide others as well). The signatures of these classes are deﬁned in the following.

12.2.1 Class Double

package scala; abstract sealed class Double extends AnyVal { def + (that: Double): Double // double addition def - (that: Double): Double // double subtraction def * (that: Double): Double // double multiplication def / (that: Double): Double // double division def % (that: Double): Double // double remainder

def == (that: Double): Boolean // double equality def != (that: Double): Boolean // double inequality def < (that: Double): Boolean // double less def > (that: Double): Boolean // double greater def <= (that: Double): Boolean // double less or equals def >= (that: Double): Boolean // double greater or equals

def - : Double = 0.0 - this // double negation def + : Double = this }

12.2.2 Class Float

package scala; abstract sealed class Float extends AnyVal { def coerce: Double // convert to Double

def + (that: Double): Double; // double addition def + (that: Float): Double // float addition /* analogous for -, *, /, % */

def == (that: Double): Boolean; // double equality def == (that: Float): Boolean; // float equality /* analogous for !=, <, >, <=, >= */

def - : Float; // float negation def + : Float 96 The Scala Standard Library

}

12.2.3 Class Long

package scala; abstract sealed class Long extends AnyVal { def coerce: Double // convert to Double def coerce: Float // convert to Float

def + (that: Double): Double; // double addition def + (that: Float): Double; // float addition def + (that: Long): Long = // long addition /* analogous for -, *, /, % */

def << (cnt: Int): Long // long left shift def >> (cnt: Int): Long // long signed right shift def >>> (cnt: Int): Long // long unsigned right shift def & (that: Long): Long // long bitwise and def | (that: Long): Long // long bitwise or def ^ (that: Long): Long // long bitwise exclusive or

def == (that: Double): Boolean; // double equality def == (that: Float): Boolean; // float equality def == (that: Long): Boolean // long equality /* analogous for !=, <, >, <=, >= */

def - : Long; // long negation def + : Long; // long identity def ~ : Long // long bitwise negation }

12.2.4 Class Int

package scala; abstract sealed class Int extends AnyVal { def coerce: Double // convert to Double def coerce: Float // convert to Float def coerce: Long // convert to Long

def + (that: Double): Double; // double addition def + (that: Float): Double; // float addtion def + (that: Long): Long; // long addition def + (that: Int): Int; // int addition /* analogous for -, *, /, % */

def << (cnt: Int): Int; // int left shift 12.2 Value Classes 97

/* analogous for >>, >>> */

def & (that: Long): Long; // long bitwise and def & (that: Int): Int; // int bitwise and /* analogous for |, ^ */

def == (that: Double): Boolean; // double equality def == (that: Float): Boolean; // float equality def == (that: Long): Boolean // long equality def == (that: Int): Boolean // int equality /* analogous for !=, <, >, <=, >= */

def - : Int; // int negation def + : Int; // int identity def ~ : Int; // int bitwise negation }

12.2.5 Class Short

package scala; abstract sealed class Short extends AnyVal { def coerce: Double // convert to Double def coerce: Float // convert to Float def coerce: Long // convert to Long def coerce: Int // convert to Int }

12.2.6 Class Char

package scala; abstract sealed class Char extends AnyVal { def coerce: Double // convert to Double def coerce: Float // convert to Float def coerce: Long // convert to Long def coerce: Int // convert to Int

def isDigit: Boolean; // is this character a digit? def isLetter: Boolean; // is this character a letter? def isLetterOrDigit: Boolean; // is this character a letter or digit? def isWhiteSpace // is this a whitespace character? }

12.2.7 Class Short

package scala; abstract sealed class Short extends AnyVal { 98 The Scala Standard Library

def coerce: Double // convert to Double def coerce: Float // convert to Float def coerce: Long // convert to Long def coerce: Int // convert to Int def coerce: Short // convert to Short }

12.2.8 Class Boolean

package scala; abstract sealed class Boolean extends AnyVal { def && (def x: Boolean): Boolean; // boolean and def || (def x: Boolean): Boolean; // boolean or def & (x: Boolean): Boolean; // boolean strict and def | (x: Boolean): Boolean // boolean strict or

def == (x: Boolean): Boolean // boolean equality def != (x: Boolean): Boolean // boolean inequality

def ! (x: Boolean): Boolean // boolean negation }

12.2.9 Class Unit

package scala; abstract sealed class Unit extends AnyVal;

12.3 Standard Reference Classes

This section presents some standard Scala reference classes which are treated in a special way in Scala compiler – either Scala provides syntactic sugar for them, or the Scala compiler generates special code for their operations. Other classes in the standard Scala library are documented by HTML pages elsewhere.

12.3.1 Class String

The String class is usually derived from the standard String class of the underlying host system (and may be identiﬁed with it). For Scala clients the class is taken to support in each case a method

def + (that: Any): String which concatenates its left operand with the textual representation of its right operand. 12.3 Standard Reference Classes 99

12.3.2 The Tuple classes

Scala deﬁnes tuple classes Tuplen for n 2, ..., 9. These are deﬁned as follows. = package scala; case class Tuplen[+a_1, ..., +a_n](_1: a_1, ..., _n: a_n){ def toString = "(" ++ _1 ++ "," ++ ... ++ "," ++_n ++ ")" }

The implicitly imported Predef object (§12.4) deﬁnes the names Pair as an alias of Tuple2 and Triple as an alias for Tuple3.

12.3.3 The Function Classes

Scala deﬁnes function classes Functionn for n 1, ..., 9. These are deﬁned as fol- = lows.

package scala; class Functionn[-a_1, ..., -a_n, +b] { def apply(x_1: a_1, ..., x_n: a_n): b; def toString = ""; }

A subclass of Function1 represents partial functions, which are undeﬁned on some points in their domain. In addition to the apply method of functions, partial functions also have a isDefined method, which tells whether the function is deﬁned at the given argument:

class PartialFunction[-a,+b] extends Function1[a, b] { def isDefinedAt(x: a): Boolean }

The implicitly imported Predef object (§12.4) deﬁnes the name Function as an alias of Function1.

12.3.4 Class Array

The class of generic arrays is given as follows.

package scala; class Array[a](length: int) with Function[Int, a] { def length: int; def apply(i: Int): a; def update(i: Int)(x: a): Unit; } 100 The Scala Standard Library

12.4 The Predef Object

The Predef module defines standard functions and type aliases for Scala programs. It is always implicitly imported, so that all its defined members are available without qualification. Here is its definition for the JVM environment.

package scala; object Predef { type byte = scala.Byte; type short = scala.Short; type char = scala.Char; type int = scala.Int; type long = scala.Long; type float = scala.Float; type double = scala.Double; type boolean = scala.Boolean; type unit = scala.Unit;

type String = java.lang.String; type NullPointerException = java.lang.NullPointerException; type Throwable = java.lang.Throwable; // other aliases to be identified

/** Abort with error message */ def error(message: String): All = throw new Error(message);

/** Throw an error if given assertion does not hold. */ def assert(assertion: Boolean): Unit = if (!assertion) throw new Error("assertion failed");

/** Throw an error with given message if given assertion does not hold */ def assert(assertion: Boolean, message: Any): Unit = { if (!assertion) throw new Error("assertion failed: " + message);

/** Create an array with given elements */ def Array[A](xs: A*): Array[A] = { val array: Array[A] = new Array[A](xs.length); var i = 0; for (val x <- xs.elements) { array(i) = x; i = i + 1; } array; }

/** Aliases for pairs and triples */ type Pair[+p, +q] = Tuple2[p, q]; def Pair[a, b](x: a, y: b) = Tuple2(x, y); type Triple[+a, +b, +c] = Tuple3[a, b, c]; 12.5 Class Node 101

def Triple[a, b, c](x: a, y: b, z: c) = Tuple3(x, y, z);

/** Alias for unary functions */ type Function = Function1;

/** Some standard simple functions */ def id[a](x: a): a = x; def fst[a](x: a, y: Any): a = x; def scd[a](x: Any, y: a): a = y; }

12.5 Class Node

package scala.xml;

trait Node {

/** the label of this node */ def label: String;

/** attribute axis */ def attribute: Map[String, String];

/** child axis (all children of this node) */ def child: Seq[Node];

/** descendant axis (all descendants of this node) */ def descendant: Seq[Node] = child.toList.flatMap { x => x::x.descendant.asInstanceOf[List[Node]] };

/** descendant axis (all descendants of this node) */ def descendant_or_self: Seq[Node] = this::child.toList.flatMap { x => x::x.descendant.asInstanceOf[List[Node]] };

override def equals(x: Any): boolean = x match { case that:Node => that.label == this.label && that.attribute.sameElements(this.attribute) && that.child.sameElements(this.child) case _ => false }; 102 The Scala Standard Library

/** XPath style projection function. Returns all children of this node * that are labelled with ’that. The document order is preserved. */ def \(that: Symbol): NodeSeq = { new NodeSeq({ that.name match { case "_" => child.toList; case _ => var res:List[Node] = Nil; for (val x <- child.elements; x.label == that.name) { res = x::res; } res.reverse } }); }

/** XPath style projection function. Returns all nodes labelled with the * name ’that from the descendant_or_self axis. Document order is preserved. */ def \\(that: Symbol): NodeSeq = { new NodeSeq( that.name match { case "_" => this.descendant_or_self; case _ => this.descendant_or_self.asInstanceOf[List[Node]]. filter(x => x.label == that.name); }) }

/** hashcode for this XML node */ override def hashCode() = Utility.hashCode(label, attribute.toList.hashCode(), child);

/** string representation of this node */ override def toString() = Utility.toXML(this);

} Bibliography

[GR83] Adele Goldberg and David Robson. Smalltalk-80; The Language and Its Implementation. Addison-Wesley, 1983. ISBN 0-201-11371-6.

[Mat01] Yukihiro Matsumoto. Ruby in a Nutshell. O’Reilly & Associates, nov 2001. ISBN 0-596-00214-9.

[OCRZ03] Martin Odersky, Vincent Cremet, Christine Röckl, and Matthias Zenger. A nominal theory of objects with dependent types. In Proc. FOOL 10, January 2003. http://www.cis.upenn.edu/~bcpierce/FOOL/FOOL10.html.

[vRD03] Guido van Rossum and Fred L. Drake. The Python Language Reference Manual. Network Theory Ltd, sep 2003. ISBN 0-954-16178-5 http://www.python.org/doc/current/ref/ref.html.

[W3Ca] W3C. Document object model (DOM). http://www.w3.org/DOM/.

[W3Cb] W3C. Extensible markup language (XML). http://www.w3.org/TR/REC-xml.

Chapter A Scala Syntax Summary

The lexical syntax of Scala is given by the following grammar in EBNF form.

upper ::= ‘A’ | ... | ‘Z’ | ‘$’ | ‘_’ and Unicode Lu lower ::= ‘a’ | ... | ‘z’ and Unicode Ll letter ::= upper | lower and Unicode categories Lo, Lt, Nl digit ::= ‘0’ | ... | ‘9’ special ::= “all other characters in \u0020-007F and Unicode categories Sm, So except parentheses ([]) and periods”

op ::= special {special} varid ::= lower {letter | digit} [‘_’ {digit} [id]] id ::= upper {letter | digit} [‘_’ {digit} [id]] | varid | op | ‘\’stringLit

intLit ::= “as in Java” floatLit ::= “as in Java” charLit ::= “as in Java” stringLit ::= “as in Java” symbolLit ::= ‘\’’ id

comment ::= ‘/*’ ‘‘any sequence of characters’’ ‘*/’ | ‘//’ ‘any sequence of characters up to end of line’’

The context-free syntax of Scala is given by the following EBNF grammar.

Literal ::= intLit | floatLit | charLit | stringLit 106 Scala Syntax Summary

| symbolLit | true | false | null

StableId ::= id | Path ‘.’ id Path ::= StableId | [id ‘.’] this | [id ’.’] super [‘[’ id ‘]’]‘.’ id

Type ::= Type1 ‘=>’ Type | ‘(’ [Types] ‘)’ ‘=>’ Type | Type1 Type1 ::= SimpleType {with SimpleType} [Refinement] SimpleType ::= SimpleType TypeArgs | SimpleType ‘#’ id | StableId | Path ‘.’ type | ‘(’ Type ’)’ TypeArgs ::= ‘[’ Types ‘]’ Types ::= Type {‘,’ Type} Refinement ::= ‘{’ [RefineStat {‘;’ RefineStat}] ‘}’ RefineStat ::= Dcl | type TypeDef |

Exprs ::= Expr {‘,’ Expr} Expr ::= Bindings ‘=>’ Expr | Expr1 Expr1 ::= if ‘(’ Expr1 ‘)’ Expr [[‘;’] else Expr] | try ‘{’ Block ‘}’ [catch Expr] [finally Expr] | do Expr [‘;’] while ‘(’ Expr ’)’ | for ‘(’ Enumerators ‘)’ [yield] Expr | return [Expr] | throw Expr | [SimpleExpr ‘.’] id ‘=’ Expr | SimpleExpr ArgumentExprs ‘=’ Expr | PostfixExpr [‘:’ Type1] | MethodClosure PostfixExpr ::= InfixExpr [id] InfixExpr ::= PrefixExpr | InfixExpr id PrefixExpr PrefixExpr ::= [‘-’ | ‘+’ | ‘~’ | ‘!’] SimpleExpr SimpleExpr ::= Literal | Path 107

| ‘(’ [Expr] ‘)’ | BlockExpr | new Template | SimpleExpr ‘.’ id | SimpleExpr TypeArgs | SimpleExpr ArgumentExprs | XmlExpr ArgumentExprs ::= ‘(’ [Exprs] ’)’ | BlockExpr MethodClosure ::= ‘.’ Id {‘.’ Id | TypeArgs | ArgumentExprs} BlockExpr ::= ‘{’ CaseClause {CaseClause} ‘}’ | ‘{’ Block ‘}’ Block ::= {BlockStat ‘;’} [ResultExpr] BlockStat ::= Import | Def | {LocalModifier} TmplDef | Expr1 | ResultExpr ::= Expr1 | Bindings ‘=>’ Block

Enumerators ::= Generator {‘;’ Enumerator} Enumerator ::= Generator | Expr Generator ::= val Pattern1 ‘<-’ Expr

CaseClause ::= case Pattern [‘if’ PostfixExpr] ‘=>’ Block

Constr ::= StableId [TypeArgs] [‘(’ [Exprs] ‘)’]

Pattern ::= Pattern1 { ‘|’ Pattern1 } Pattern1 ::= varid ‘:’ Type | ‘_’ ‘:’ Type | Pattern2 Pattern2 ::= [varid ‘@’] Pattern3 Pattern3 ::= SimplePattern [ ’*’ | ’?’ | ’+’ ] | SimplePattern { id SimplePattern } SimplePattern ::= ‘_’ | varid | Literal | StableId [ ‘(’ [Patterns] ‘)’ ] | ‘(’ [Patterns] ‘)’ | XmlPattern Patterns ::= Pattern {‘,’ Pattern}

TypeParamClause ::= ‘[’ VarTypeParam {‘,’ VarTypeParam} ‘]’ 108 Scala Syntax Summary

FunTypeParamClause ::= ‘[’ TypeParam {‘,’ TypeParam} ‘]’ VarTypeParam ::= [‘+’ | ‘-’] TypeParam TypeParam ::= id [>: Type] [<: Type | <% Type] ParamClause ::= ‘(’ [Param {‘,’ Param}] ‘)’ ClassParamClause::= ‘(’ [ClassParam {‘,’ ClassParam}] ‘)’ Param ::= id ‘:’ [‘=>’ Type [‘*’] ClassParam ::= [{Modifier} ‘val’] Param Bindings ::= id [‘:’ Type1] | ‘(’ Binding {‘,’ Binding ‘)’ Binding ::= id [‘:’ Type]

AttributeClause ::= ‘[’ Attribute {‘,’ Attribute} ‘]’ Attribute ::= Constr

Template ::= Constr {‘with’ Constr} [TemplateBody] TemplateBody ::= ‘{’ [TemplateStat {‘;’ TemplateStat}] ‘}’ TemplateStat ::= Import | {AttributeClause} {Modifier} Def | {AttributeClause} {Modifier} Dcl | Expr |

Dcl ::= val ValDcl | var VarDcl | def FunDcl | type TypeDcl

ValDcl ::= id {‘,’ id} ‘:’ Type VarDcl ::= id {‘,’ id} ‘:’ Type FunDcl ::= FunSig {‘,’ FunSig} ‘:’ Type FunSig ::= id [FunTypeParamClause] {ParamClause} TypeDcl ::= id [>: Type] [<: Type] 109

Def ::= val PatDef | var VarDef | def FunDef | type TypeDef | TmplDef PatDef ::= Pattern2 {‘,’ Pattern2} [‘:’ Type] ‘=’ Expr VarDef ::= id {‘,’ id} [‘:’ Type] ‘=’ Expr | id {‘,’ id} ‘:’ Type ‘=’ ‘_’ FunDef ::= FunSig {‘,’ FunSig} ‘:’ Type ‘=’ Expr | this ParamClause ‘=’ ConstrExpr TypeDef ::= id [TypeParamClause] ‘=’ Type

TmplDef ::= ([case] class | trait) ClassDef | [case] object ObjectDef ClassDef ::= ClassSig {‘,’ ClassSig} [‘:’ SimpleType] ClassTemplate ClassSig ::= id [TypeParamClause] [ClassParamClause] ObjectDef ::= id {‘,’ id} [‘:’ SimpleType] ClassTemplate

ClassTemplate ::= extends Template | TemplateBody | ConstrExpr ::= this ArgumentExprs | ‘{’ this ArgumentExprs {‘;’ BlockStat} ‘}’

CompilationUnit ::= [package QualId ‘;’] {TopStat ‘;’} TopStat TopStat ::= {AttributeClause} {Modifier} TmplDef | Import | Packaging | Packaging ::= package QualId ‘{’ {TopStat ‘;’} TopStat ‘}’ QualId ::= id {‘.’ id}

Chapter B Implementation Status

The present Scala compiler does not yet implement all of the Scala speciﬁcation. Its currently existing omissions and deviations are listed below. We are working on a reﬁned implementation that addresses these issues.

1. Unicode support is still limited. At present we only permit Unicode encod- ings \uXXXX in strings and backquote-enclosed identifiers. To define or access a Unicode identifier, you need to put it in backquotes and use the \uXXXX en- coding.

2. The unicode operator “ ” (§1.1) is not yet recognized; you need to use the ⇒ two character ASCII equivalent “=>” instead.

3. The current implementation does not yet support run-time types. All types are erased (§3.6) during compilation. This means that the following operations give potentially wrong results.

• Type tests and type casts to parameterized types. Here it is only tested that a value is an instance of the given top-level type constructor. • Type tests and type casts to type parameters and abstract types. Here it is only tested that a value is an instance of the type parameter’s upper bound. • Polymorphic array creation. If t is a type variable or abstract type, then new Array[t] will yield an array of the upper bound of t.

4. Return expressions are not yet permitted inside an anonymous function or inside a call-by-name argument (i.e. a function argument corresponding to a def parameter).

5. Members of the empty package (§9.1) cannot yet be accessed from other source ﬁles. Hence, all library classes and objects have to be in some package. 112 Implementation Status

6. At present, auxiliary constructors (§5.2.1) are only permitted for monomorphic classes. 7. The Array class supports as yet only a restricted set of operations as given in §12.3.4. It is planned to extend that interface. In particular, arrays will implement the scala.Seq trait as well as the methods needed to support for- comprehensions. 8. At present, all classes used as mixins must be accessible to the Scala compiler in source form.